1<!DOCTYPE html> 2<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head> 3 4<meta charset="utf-8"> 5<meta name="generator" content="quarto-1.10.18"> 6 7<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes"> 8 9 10<title>Research Projects â Paul Bürkner</title> 11<style> 12/* Default styles provided by pandoc. 13** See https://pandoc.org/MANUAL.html#variables-for-html for config info. 14*/ 15span.smallcaps{font-variant: small-caps;} 16div.columns{display: flex; gap: 1.5em;} 17div.column{flex: auto;} 18@media screen { 19div.columns{gap: min(4vw, 1.5em);} 20div.column{overflow-x: auto;} 21} 22div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;} 23ul.task-list{list-style: none;} 24ul.task-list li input[type="checkbox"] { 25 width: 0.8em; 26 margin: 0 0.8em 0.2em -1em; /* quarto-specific, see https://github.com/quarto-dev/quarto-cli/issues/4556 */ 27 vertical-align: middle; 28} 29</style> 30 31
32<script src="../site_libs/quarto-nav/quarto-nav.js"></script>
vendor: 1 bytes, line 32
32
33<script src="../site_libs/clipboard/clipboard.min.js"></script>
vendor: 1 bytes, line 33
33
34<script src="../site_libs/quarto-search/autocomplete.umd.js"></script>
vendor: 1 bytes, line 34
34
35<script src="../site_libs/quarto-search/fuse.min.js"></script>
vendor: 1 bytes, line 35
35
36<script src="../site_libs/quarto-search/quarto-search.js"></script>
36 37<meta name="quarto:offset" content="../">
38<script src="../site_libs/quarto-html/quarto.js" type="module"></script>
vendor: 1 bytes, line 38
38
39<script src="../site_libs/quarto-html/tabsets/tabsets.js" type="module"></script>
vendor: 1 bytes, line 39
39
40<script src="../site_libs/quarto-html/popper.min.js"></script>
vendor: 1 bytes, line 40
40
41<script src="../site_libs/quarto-html/tippy.umd.min.js"></script>
vendor: 1 bytes, line 41
41
42<script src="../site_libs/quarto-html/anchor.min.js"></script>
42 43<link href="../site_libs/quarto-html/tippy.css" rel="stylesheet"> 44<link href="../site_libs/quarto-html/quarto-syntax-highlighting-64a204ab8560d761af7679ceaba22944.css" rel="stylesheet" class="quarto-color-scheme" id="quarto-text-highlighting-styles"> 45<link href="../site_libs/quarto-html/quarto-syntax-highlighting-dark-b85bc7c33db8c58e0ec93c3465666fed.css" rel="stylesheet" class="quarto-color-scheme quarto-color-alternate" id="quarto-text-highlighting-styles"> 46<link href="../site_libs/quarto-html/quarto-syntax-highlighting-64a204ab8560d761af7679ceaba22944.css" rel="stylesheet" class="quarto-color-scheme-extra" id="quarto-text-highlighting-styles">
47<script src="../site_libs/bootstrap/bootstrap.min.js"></script>
47 48<link href="../site_libs/bootstrap/bootstrap-icons.css" rel="stylesheet"> 49<link href="../site_libs/bootstrap/bootstrap-28d97e500b70ae5f6a2f7d5a210b94b3.min.css" rel="stylesheet" append-hash="true" class="quarto-color-scheme" id="quarto-bootstrap" data-mode="light"> 50<link href="../site_libs/bootstrap/bootstrap-dark-f3b788dbfadee4b7a335ed7e694d9a72.min.css" rel="stylesheet" append-hash="true" class="quarto-color-scheme quarto-color-alternate" id="quarto-bootstrap" data-mode="dark"> 51<link href="../site_libs/bootstrap/bootstrap-28d97e500b70ae5f6a2f7d5a210b94b3.min.css" rel="stylesheet" append-hash="true" class="quarto-color-scheme-extra" id="quarto-bootstrap" data-mode="light"> 52<link href="../site_libs/quarto-contrib/fontawesome6-0.1.0/all.css" rel="stylesheet"> 53<link href="../site_libs/quarto-contrib/fontawesome6-0.1.0/latex-fontsize.css" rel="stylesheet">
54<script src="../site_libs/quarto-contrib/iconify-2.1.0/iconify-icon.min.js"></script>
vendor: 1 bytes, line 54
54
55<script id="quarto-search-options" type="application/json">{ 56 "location": "navbar", 57 "copy-button": false, 58 "collapse-after": 3, 59 "panel-placement": "end", 60 "type": "textbox", 61 "limit": 50, 62 "keyboard-shortcut": [ 63 "f", 64 "/", 65 "s" 66 ], 67 "language": { 68 "search-no-results-text": "No results", 69 "search-matching-documents-text": "matching documents", 70 "search-copy-link-title": "Copy link to search", 71 "search-hide-matches-text": "Hide additional matches", 72 "search-more-match-text": "more match in this document", 73 "search-more-matches-text": "more matches in this document", 74 "search-clear-button-title": "Clear", 75 "search-text-placeholder": "", 76 "search-detached-cancel-button-title": "Cancel", 77 "search-submit-button-title": "Submit", 78 "search-label": "Search" 79 } 80}</script>
80 81 82 83<link rel="stylesheet" href="../styles.css"> 84</head> 85 86<body class="nav-fixed quarto-light">
86<script id="quarto-html-before-body" type="application/javascript"> 87 const toggleBodyColorMode = (bsSheetEl) => { 88 const mode = bsSheetEl.getAttribute("data-mode"); 89 const bodyEl = window.document.querySelector("body"); 90 if (mode === "dark") { 91 bodyEl.classList.add("quarto-dark"); 92 bodyEl.classList.remove("quarto-light"); 93 } else { 94 bodyEl.classList.add("quarto-light"); 95 bodyEl.classList.remove("quarto-dark"); 96 } 97 } 98 const toggleBodyColorPrimary = () => { 99 const bsSheetEl = window.document.querySelector("link#quarto-bootstrap:not([rel=disabled-stylesheet])"); 100 if (bsSheetEl) { 101 toggleBodyColorMode(bsSheetEl); 102 } 103 } 104 const setColorSchemeToggle = (alternate) => { 105 const toggles = window.document.querySelectorAll('.quarto-color-scheme-toggle'); 106 for (let i=0; i < toggles.length; i++) { 107 const toggle = toggles[i]; 108 if (toggle) { 109 if (alternate) { 110 toggle.classList.add("alternate"); 111 } else { 112 toggle.classList.remove("alternate"); 113 } 114 } 115 } 116 }; 117 const toggleColorMode = (alternate) => { 118 // Switch the stylesheets 119 const primaryStylesheets = window.document.querySelectorAll('link.quarto-color-scheme:not(.quarto-color-alternate)'); 120 const alternateStylesheets = window.document.querySelectorAll('link.quarto-color-scheme.quarto-color-alternate'); 121 manageTransitions('#quarto-margin-sidebar .nav-link', false); 122 if (alternate) { 123 // note: dark is layered on light, we don't disable primary! 124 enableStylesheet(alternateStylesheets); 125 for (const sheetNode of alternateStylesheets) { 126 if (sheetNode.id === "quarto-bootstrap") { 127 toggleBodyColorMode(sheetNode); 128 } 129 } 130 } else { 131 disableStylesheet(alternateStylesheets); 132 enableStylesheet(primaryStylesheets) 133 toggleBodyColorPrimary(); 134 } 135 manageTransitions('#quarto-margin-sidebar .nav-link', true); 136 // Switch the toggles 137 setColorSchemeToggle(alternate) 138 // Hack to workaround the fact that safari doesn't 139 // properly recolor the scrollbar when toggling (#1455) 140 if (navigator.userAgent.indexOf('Safari') > 0 && navigator.userAgent.indexOf('Chrome') == -1) { 141 manageTransitions("body", false); 142 window.scrollTo(0, 1); 143 setTimeout(() => { 144 window.scrollTo(0, 0); 145 manageTransitions("body", true); 146 }, 40); 147 } 148 } 149 const disableStylesheet = (stylesheets) => { 150 for (let i=0; i < stylesheets.length; i++) { 151 const stylesheet = stylesheets[i]; 152 stylesheet.rel = 'disabled-stylesheet'; 153 } 154 } 155 const enableStylesheet = (stylesheets) => { 156 for (let i=0; i < stylesheets.length; i++) { 157 const stylesheet = stylesheets[i]; 158 if(stylesheet.rel !== 'stylesheet') { // for Chrome, which will still FOUC without this check 159 stylesheet.rel = 'stylesheet'; 160 } 161 } 162 } 163 const manageTransitions = (selector, allowTransitions) => { 164 const els = window.document.querySelectorAll(selector); 165 for (let i=0; i < els.length; i++) { 166 const el = els[i]; 167 if (allowTransitions) { 168 el.classList.remove('notransition'); 169 } else { 170 el.classList.add('notransition'); 171 } 172 } 173 } 174 const isFileUrl = () => { 175 return window.location.protocol === 'file:'; 176 } 177 const hasAlternateSentinel = () => { 178 let styleSentinel = getColorSchemeSentinel(); 179 if (styleSentinel !== null) { 180 return styleSentinel === "alternate"; 181 } else { 182 return false; 183 } 184 } 185 const setStyleSentinel = (alternate) => { 186 const value = alternate ? "alternate" : "default"; 187 if (!isFileUrl()) { 188 window.localStorage.setItem("quarto-color-scheme", value); 189 } else { 190 localAlternateSentinel = value; 191 } 192 } 193 const getColorSchemeSentinel = () => { 194 if (!isFileUrl()) { 195 const storageValue = window.localStorage.getItem("quarto-color-scheme"); 196 return storageValue != null ? storageValue : localAlternateSentinel; 197 } else { 198 return localAlternateSentinel; 199 } 200 } 201 const toggleGiscusIfUsed = (isAlternate, darkModeDefault) => { 202 const baseTheme = document.querySelector('#giscus-base-theme')?.value ?? 'light'; 203 const alternateTheme = document.querySelector('#giscus-alt-theme')?.value ?? 'dark'; 204 let newTheme = ''; 205 if(authorPrefersDark) { 206 newTheme = isAlternate ? baseTheme : alternateTheme; 207 } else { 208 newTheme = isAlternate ? alternateTheme : baseTheme; 209 } 210 const changeGiscusTheme = () => { 211 // From: https://github.com/giscus/giscus/issues/336 212 const sendMessage = (message) => { 213 const iframe = document.querySelector('iframe.giscus-frame'); 214 if (!iframe) return; 215 iframe.contentWindow.postMessage({ giscus: message }, 'https://giscus.app'); 216 } 217 sendMessage({ 218 setConfig: { 219 theme: newTheme 220 } 221 }); 222 } 223 const isGiscussLoaded = window.document.querySelector('iframe.giscus-frame') !== null; 224 if (isGiscussLoaded) { 225 changeGiscusTheme(); 226 } 227 }; 228 const authorPrefersDark = false;
229 const darkModeDefault = authorPrefersDark; 230 document.querySelector('link#quarto-text-highlighting-styles.quarto-color-scheme-extra').rel = 'disabled-stylesheet'; 231 document.querySelector('link#quarto-bootstrap.quarto-color-scheme-extra').rel = 'disabled-stylesheet'; 232 let localAlternateSentinel = darkModeDefault ? 'alternate' : 'default'; 233 // Dark / light mode switch 234 window.quartoToggleColorScheme = () => { 235 // Read the current dark / light value 236 let toAlternate = !hasAlternateSentinel(); 237 toggleColorMode(toAlternate); 238 setStyleSentinel(toAlternate); 239 toggleGiscusIfUsed(toAlternate, darkModeDefault); 240 window.dispatchEvent(new Event('resize')); 241 }; 242 // Switch to dark mode if need be 243 if (hasAlternateSentinel()) { 244 toggleColorMode(true); 245 } else { 246 toggleColorMode(false); 247 } 248 </script>
248 249 250<div id="quarto-search-results"></div> 251 <header id="quarto-header" class="headroom fixed-top"> 252 <nav class="navbar navbar-expand-lg " data-bs-theme="dark"> 253 <div class="navbar-container container-fluid"> 254 <div class="navbar-brand-container mx-auto"> 255 <a class="navbar-brand" href="../index.html"> 256 <span class="navbar-title">Paul Bürkner</span> 257 </a> 258 </div> 259 <div id="quarto-search" class="" title="Search"></div> 260 <button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarCollapse" aria-controls="navbarCollapse" role="menu" aria-expanded="false" aria-label="Toggle navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }"> 261 <span class="navbar-toggler-icon"></span> 262</button> 263 <div class="collapse navbar-collapse" id="navbarCollapse"> 264 <ul class="navbar-nav navbar-nav-scroll me-auto"> 265 <li class="nav-item"> 266 <a class="nav-link" href="../research/index.html"> 267<span class="menu-text">Research</span></a> 268 </li> 269 <li class="nav-item"> 270 <a class="nav-link" href="../people/index.html"> 271<span class="menu-text">People</span></a> 272 </li> 273 <li class="nav-item"> 274 <a class="nav-link active" href="../projects/index.html" aria-current="page"> 275<span class="menu-text">Projects</span></a> 276 </li> 277 <li class="nav-item"> 278 <a class="nav-link" href="../publications/index.html"> 279<span class="menu-text">Publications</span></a> 280 </li> 281 <li class="nav-item"> 282 <a class="nav-link" href="../software/index.html"> 283<span class="menu-text">Software</span></a> 284 </li> 285 <li class="nav-item"> 286 <a class="nav-link" href="../talks/index.html"> 287<span class="menu-text">Talks</span></a> 288 </li> 289 <li class="nav-item"> 290 <a class="nav-link" href="../theses/index.html"> 291<span class="menu-text">Theses</span></a> 292 </li> 293 <li class="nav-item"> 294 <a class="nav-link" href="../positions/index.html"> 295<span class="menu-text">Positions</span></a> 296 </li> 297 <li class="nav-item"> 298 <a class="nav-link" href="../cv/index.html"> 299<span class="menu-text">CV</span></a> 300 </li> 301</ul> 302 <ul class="navbar-nav navbar-nav-scroll ms-auto"> 303 <li class="nav-item"> 304 <a class="nav-link" href="mailto:[email protected]"> 305<span class="menu-text"><i class="fa-solid fa-envelope" aria-label="envelope"></i></span></a> 306 </li> 307 <li class="nav-item compact"> 308 <a class="nav-link" href="https://github.com/paul-buerkner"> <i class="bi bi-github" role="img" aria-label="github"> 309</i> 310<span class="menu-text"></span></a> 311 </li> 312 <li class="nav-item"> 313 <a class="nav-link" href="https://scholar.google.com/citations?user=JSj6m1IAAAAJ&hl"> 314<span class="menu-text"><i class="fa-solid fa-graduation-cap" aria-label="graduation-cap"></i></span></a> 315 </li> 316 <li class="nav-item"> 317 <a class="nav-link" href="https://bsky.app/profile/paulbuerkner.com"> 318<span class="menu-text"><iconify-icon role="img" inline="" icon="fa6-brands:bluesky" aria-label="Icon bluesky from fa6-brands Iconify.design set." title="Icon bluesky from fa6-brands Iconify.design set."></iconify-icon></span></a> 319 </li> 320</ul> 321 </div> <!-- /navcollapse --> 322 <div class="quarto-navbar-tools"> 323 <a href="" class="quarto-color-scheme-toggle quarto-navigation-tool px-1" onclick="window.quartoToggleColorScheme(); return false;" title="Toggle dark mode"><i class="bi"></i></a> 324</div> 325 </div> <!-- /container-fluid --> 326 </nav> 327</header> 328<!-- content --> 329<div id="quarto-content" class="quarto-container page-columns page-rows-contents page-layout-full page-navbar"> 330<!-- sidebar --> 331<!-- margin-sidebar --> 332 <div id="quarto-margin-sidebar" class="sidebar margin-sidebar zindex-bottom"> 333 334 </div> 335<!-- main --> 336<main class="content column-page" id="quarto-document-content"> 337 338 339<header id="title-block-header" class="quarto-title-block default"> 340<div class="quarto-title"> 341<h1 class="title">Research Projects</h1> 342</div> 343 344 345 346<div class="quarto-title-meta column-page"> 347 348 349 350 351 </div> 352 353 354 355</header> 356 357 358<p>Here you can find an overview of my current research projects. A list of past research projects can be found at the <a href="#past-projects">bottom of this page</a>.</p> 359<section id="grammo" class="level2"> 360<h2 class="anchored" data-anchor-id="grammo">grammo: A grammar of probabilistic models</h2> 361<p>This project aims to design and implement grammo: a novel mid-level grammar for expressing Bayesian statistical models. Grammo will provide substantially more flexibility, reusability and transparency than state-of-the-art high-level statistical packages while staying much more concise and accessible than low-level probabilistic programming languages. Beyond theoretical analysis of its properties, the usability of grammo will be evaluated with human users. We will then develop new methods for automatic and computer-assisted analysis, manipulation and debugging of probabilistic programs, using grammo as a testbed. Further, grammo will allow us to research several classes of complex models that are currently rarely used due to difficulties in their specification. This includes various forms of joint models comb
361ining multiple data-generating mechanisms in a single model with shared parameters as well as time-to-event models and non-standard structural equation models. We will then develop workflows and supporting tools for those models including prior choice, model validation and selection.</p> 362<p>Overarching Topics: <a href="../research#machine-workflow" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Machine-Assisted Workflows</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 363<p>Project Members: <a href="../people#daniel-habermann" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Daniel Habermann</a></p> 364<p>Funders: <a href="https://www.dfg.de/en/index.jsp" class="btn btn-outline-primary btn-page-header btn-xs" role="button">German Research Foundation (DFG)</a> <a href="https://gacr.cz/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Czech Science Foundation (GACR)</a></p> 365<p>Funding Period: 2026 â 2029</p> 366<!-- Publications: --> 367<!-- --> 368</section> 369<section id="deep-bayes-biomed" class="level2"> 370<h2 class="anchored" data-anchor-id="deep-bayes-biomed">Deep Bayes in Biomedicine</h2> 371<p>Progress in biomedical research is limited by three challenges: (1) the systems we study, like the immune system or the brain, are complex and variable; (2) experiments often have small sample sizes because of ethical or cost constraints; and (3) the effects we look for are often small, comparable to normal biological variation.</p> 372<p>Bayesian statistics is a powerful approach for tackling such problems, allowing inclusion of prior knowledge and principled uncertainty quantification. This makes conclusions more reliable and reproducible. However, Bayesian inference is computationally far more expensive than conventional data analyses, limiting its practicality for modern biomedical experiments.</p> 373<p>Amortized Bayesian Inference (ABI), an approach based on deep learning, removes this barrier. By âlearningâ in advance how to perform Bayesian inference, ABI can analyze new datasets almost instantly. It matches or exceeds the speed of conventional methods while retaining the full advantages of Bayesian inference. This project applies ABI to challenging biomedical workflows in immunology and neuroscience, where current tools fall short. By combining expertise from biomedicine, deep learning, and statistics, we make ABI easier to use and adapt, enabling researchers to gain biomedical insights faster and more reliably.</p> 374<p>Overarching Topics: <a href="../research#abi" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Amortized Inference</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 375<p>Project Members: <a href="../people#yiming-zang" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Yiming Zang</a></p> 376<p>Funders: <a href="https://www.uaruhr.de/en/research/research-support/mercur-project-funding/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">MERCUR Foundation</a> <a href="https://www.tu-dortmund.de/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">TU Dortmund University</a></p> 377<p>Funding Period: 2026 â 2029</p> 378<!-- Publications: --> 379<!-- --> 380</section> 381<section id="abi-logistics" class="level2"> 382<h2 class="anchored" data-anchor-id="abi-logistics">Real-Time Spatio-Temporal Data Analysis for Monitoring Logistics Networks</h2> 383<div class="quarto-figure quarto-figure-left"> 384<figure class="figure"> 385<p><img src="../images/ABI_graph_data.png" class="img-fluid quarto-figure quarto-figure-left figure-img" style="width:100.0%" alt="An illustration of amortized Bayesian inference for graph data."></p> 386</figure> 387</div> 388<p>In complex logistics and supply chain networks, the acquisition of tracking data representing the flow of entities through the networks has become state of the art. The goal of tracking entities is to improve transparency and predict the state of the network. An important value for operations is the estimated time of arrival of entities at different nodes of the network. The respective business goal determines the requirements for the forecasting procedure: it might be necessary to detect a delay in a container ship transport as early as possible (weeks before the arrival) to be able to send a replacement for urgent parts by air. Or it might be necessary to predict the arrival of trucks within the next hour as accurately as possible to manage the traffic at logistics sites. However, acquiring data is costly in terms of money, energy used by sensors, and required IT infrastru
388cture.</p> 389<p>In this project, we will develop new methods for predicting arrival times in complex logistics networks (e.g., multi-modal transport networks). Our methods will enable (a) the integration of different data types, e.g., event, weather, and tracing data, (b) the ability to cope with changes in the underlying logistics network in real-time, and (c) the ability to communicate uncertainty in predictions, especially in case of tracing data or weather forecasts of limited reliability.</p> 390<p>This project is part of the <a href="https://trr391.tu-dortmund.de/">Collaborative Research Center 391</a> funded by the German Research Foundation.</p> 391<p>Overarching Topics: <a href="../research#abi" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Amortized Inference</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 392<p>Project Members: <a href="../people#svenja-jedhoff" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Svenja Jedhoff</a></p> 393<p>Funders: <a href="https://www.dfg.de/en/index.jsp" class="btn btn-outline-primary btn-page-header btn-xs" role="button">German Research Foundation (DFG)</a> <a href="https://www.tu-dortmund.de/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">TU Dortmund University</a></p> 394<p>Funding Period: 2024 â 2028</p> 395<p>Publications:</p> 396<ul> 397<li><p><strong>Jedhoff, S.</strong>, Kutabi, H., Meyer, A., Bürkner, P. C. (in review). Efficient Uncertainty Propagation in Bayesian Two-Step Procedures. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2505.10510" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/sjedhoff/efficient-2step-uncertainty-paper" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{jedhoff2026efficient,&#10; author = {Jedhoff, S. and Kutabi, H. and Meyer, A. and Bürkner, P. C.},&#10; title = {Efficient Uncertainty Propagation in Bayesian Two-Step Procedures},&#10; journal = {ArXiv preprint},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 398<li><p>Kühmichel, L., Huang, J. M., Pratz, V., Arruda, J., Olischläger, H., Habermann, D., Kucharský, Å ., Elsemüller, L., Mishra, A., Bracher, N., <strong>Jedhoff, S.</strong>, Schmitt, M., Bürkner, P. C., Radev, S. T. (in review). BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2602.07098" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://bayesflow.org/main/index.html" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Software</a> <a href="https://github.com/bayesflow-org/bf2-paper-case-study" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{kuehmichel2026bayesflow,&#10; author = {Kühmichel, L. and Huang, J. M. and Pratz, V. and Arruda, J. and Olischläger, H. and Habermann, D. and Kucharský, Å . and Elsemüller, L. and Mishra, A. and Bracher, N. and Jedhoff, S. and Schmitt, M. and Bürkner, P. C. and Radev, S. T.},&#10; title = {BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python},&#10; journal = {ArXiv preprint},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 399<li><p>Riha, A. E., <strong>Jedhoff, S.</strong>, Bürkner, P. C., Vehtari, A. (in review). Approximating Bayesian Leave-One-Group-out Cross-Validation. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2609.05713" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{riha2026logo,&#10; author = {Riha, A. E. and Jedhoff, S. and Bürkner, P. C. and Vehtari, A.},&#10; title = {Approximating Bayesian Leave-One-Group-out Cross-Validation},&#10; journal = {ArXiv preprint},&#10; year = {}&#10;}" role="button">BibTeX</span></p></li> 400<li><p><strong>Jedhoff, S.</strong>, Semenova, E., Raulo, A., Meyer, A., Bürkner, P. C. (2026). From Mice to Trains: Amortized Bayesian Inference on Graph Data. <em>Transactions in Machine Learning Research</em>. <a href="../publications/pdf/2026__Jedhoff_et_al__TMLR.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://openreview.net/forum?id=vpIeCm7YEA" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2601.02241" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/sjedhoff/ABI-graph-paper" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{jedhoff2026mice,&#10;
400 author = {Jedhoff, S. and Semenova, E. and Raulo, A. and Meyer, A. and Bürkner, P. C.},&#10; title = {From Mice to Trains: Amortized Bayesian Inference on Graph Data},&#10; journal = {Transactions in Machine Learning Research},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 401</ul> 402<!-- --> 403</section> 404<section id="semi-supervised-abi" class="level2"> 405<h2 class="anchored" data-anchor-id="semi-supervised-abi">Semi-Supervised Learning for Robust Amortized Bayesian Inference</h2> 406<div class="quarto-figure quarto-figure-left"> 407<figure class="figure"> 408<p><img src="../images/self_consistency_workflow.png" class="img-fluid quarto-figure quarto-figure-left figure-img" style="width:80.0%" alt="Results obtained from semi-supervised ABI training."></p> 409</figure> 410</div> 411<p>Amortized Bayesian inference (ABI) with neural networks can solve probabilistic inverse problems orders of magnitude faster than classical methods. However, ABI is not yet sufficiently robust for widespread and safe application. When performing inference on observations outside the scope of the simulated training data, posterior approximations are likely to become highly biased, which cannot be adequately corrected just by additional simulations.</p> 412<p>In this project, we work on semi-supervised approaches that enable training not only on labeled simulated data generated from the model, but also on data originating from any source, including real-world data. We hypothesize that such approaches can strongly increase estimation accuracy and robustness especially for real-world data outside of the immediate simulation scope.</p> 413<p>Overarching Topics: <a href="../research#abi" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Amortized Inference</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 414<p>Project Members: <a href="../people#aayush-mishra" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Aayush Mishra</a></p> 415<p>Funders: <a href="https://www.tu-dortmund.de/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">TU Dortmund University</a></p> 416<p>Funding Period: 2024 â 2027</p> 417<p>Publications:</p> 418<ul> 419<li><p>Kucharský, Å ., <strong>Mishra, A.</strong>, Habermann, D., Radev, S. T., Bürkner, P. C. (in review). Improving the Accuracy of Amortized Model Comparison with Self-Consistency. <em>ArXiv preprint</em>. Short version accepted at <em>NeurIPS Workshop on Reliable Machine Learning from Unreliable Data</em>. <a href="https://arxiv.org/abs/2508.20614" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{kucharsky2026improving,&#10; author = {Kucharský, Å . and Mishra, A. and Habermann, D. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Improving the Accuracy of Amortized Model Comparison with Self-Consistency},&#10; journal = {ArXiv preprint},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 420<li><p>Kühmichel, L., Huang, J. M., Pratz, V., Arruda, J., Olischläger, H., Habermann, D., Kucharský, Å ., Elsemüller, L., <strong>Mishra, A.</strong>, Bracher, N., Jedhoff, S., Schmitt, M., Bürkner, P. C., Radev, S. T. (in review). BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2602.07098" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://bayesflow.org/main/index.html" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Software</a> <a href="https://github.com/bayesflow-org/bf2-paper-case-study" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{kuehmichel2026bayesflow,&#10; author = {Kühmichel, L. and Huang, J. M. and Pratz, V. and Arruda, J. and Olischläger, H. and Habermann, D. and Kucharský, Å . and Elsemüller, L. and Mishra, A. and Bracher, N. and Jedhoff, S. and Schmitt, M. and Bürkner, P. C. and Radev, S. T.},&#10; title = {BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python},&#10; journal = {ArXiv preprint},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 421<li><p><strong>Mishra, A.</strong>, Kucharský, Å ., Bürkner, P. C. (in review). Unsupervised Continual Learning for Amortized Bayesian Inference. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2602.22884" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mishra2026CL,&#10; author = {Mishra, A. and Kucharský, Å . and Bürkner, P. C.},&#10; title = {Unsupervised Continual Learning for Amortized Bayesian Inference},&#10; journal = {ArXiv preprint},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 422<li><p><strong>Mishra, A.</strong>, Habermann, D., Schmitt, M., Radev, S. T., Bürkner, P. C. (2026). Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data. <em>International Conference on Learning Representations (ICLR)</em>. <a href="../publications/pdf/2026__Mishra_et_al__ICLR.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://openreview.net/forum?id=RwKyg5BcgN" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2501.13483" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="http://github.com/bayesflow-org/self-consistency-real" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mishra2026robust,&#10; author = {Mishra, A. and Habermann, D. and Schmitt, M. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data},&#10; journal = {International Conference on Learning Representations (ICLR)},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 423</ul> 424<!-- --> 425</section> 426<section id="bayesflow-sim-intelligence" class="level2"> 427<h2 class="anchored" data-anchor-id="bayesflow-sim-intelligence">BayesFlow: Simulation Intelligence with Deep Learning</h2> 428<div class="quarto-figure quarto-figure-left"> 429<figure class="figure"> 430<p><img src="../images/bayesflow_overview.png" class="img-fluid quarto-figure quarto-figure-left figure-img" style="width:80.0%" alt="An illustration of the Bayesflow framework."></p> 431</figure> 432</div> 433<p>Simulation intelligence (SI) subsumes an emerging generation of scientific methods which utilize digital simulations for emulating and understanding complex real-world systems and phenomena. Recently, neural networks and deep learning have demonstrated a great potential for accelerating and scaling up SI to previously intractable problems and data sets. However, the availability of user-friendly software is still limited, which hampers the widespread and flexible use of modern SI methods.</p> 434<p>In this project, we focus on software for amortized Bayesian inference, which is an essential part of SI. The hallmark feature of amortized Bayesian inference is an upfront training phase (e.g., of a neural network), which is then amortized by a nearly instant fully Bayesian inference for an arbitrary number of data sets during test time. Concretely, we aim to advance the <a href="../software#bayesflow">BayesFlow research software library</a> into becoming the long-term, gold-standard software for amortized Bayesian inference.</p> 435<p>Overarching Topics: <a href="../research#abi" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Amortized Inference</a> <a href="../research#machine-workflow" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Machine-Assisted Workflows</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 436<p>Project Members: <a href="../people#lars-kuehmichel" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Lars Kühmichel</a> <a href="../people#Hans-olischlaeger" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Hans Olischläger</a></p> 437<p>
437Funders: <a href="https://www.dfg.de/en/index.jsp" class="btn btn-outline-primary btn-page-header btn-xs" role="button">German Research Foundation (DFG)</a> <a href="https://www.tu-dortmund.de/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">TU Dortmund University</a></p> 438<p>Funding Period: 2024 â 2028</p> 439<p>Publications:</p> 440<ul> 441<li><p><strong>Kühmichel, L.</strong>, Huang, J. M., Pratz, V., Arruda, J., <strong>Olischläger, H.</strong>, Habermann, D., Kucharský, Å ., Elsemüller, L., Mishra, A., Bracher, N., Jedhoff, S., Schmitt, M., Bürkner, P. C., Radev, S. T. (in review). BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2602.07098" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://bayesflow.org/main/index.html" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Software</a> <a href="https://github.com/bayesflow-org/bf2-paper-case-study" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{kuehmichel2026bayesflow,&#10; author = {Kühmichel, L. and Huang, J. M. and Pratz, V. and Arruda, J. and Olischläger, H. and Habermann, D. and Kucharský, Å . and Elsemüller, L. and Mishra, A. and Bracher, N. and Jedhoff, S. and Schmitt, M. and Bürkner, P. C. and Radev, S. T.},&#10; title = {BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python},&#10; journal = {ArXiv preprint},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 442<li><p>Müller, J., <strong>Kühmichel, L.</strong>, Rohbeck, M., Radev, S. T., Köthe, U. (in review). Towards Context-Aware Domain Generalization: Understanding the Benefits and Limits of Marginal Transfer Learning. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2312.10107" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mueller2025towards,&#10; author = {Müller, J. and Kühmichel, L. and Rohbeck, M. and Radev, S. T. and Köthe, U.},&#10; title = {Towards Context-Aware Domain Generalization: Understanding the Benefits and Limits of Marginal Transfer Learning},&#10; journal = {ArXiv preprint},&#10; year = {2025}&#10;}" role="button">BibTeX</span></p></li> 443<li><p>Bracher, N., <strong>Kühmichel, L.</strong>, Ivanova, D. R., Intes, X., Bürkner, P. C., Radev, S. T. (accepted). JADAI: Jointly Amortizing Adaptive Design and Bayesian Inference. <em>Proceedings of the International Conference on Machine Learning (ICML)</em>. <a href="https://arxiv.org/abs/2512.22999" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{bracher2025jadai,&#10; author = {Bracher, N. and Kühmichel, L. and Ivanova, D. R. and Intes, X. and Bürkner, P. C. and Radev, S. T.},&#10; title = {JADAI: Jointly Amortizing Adaptive Design and Bayesian Inference},&#10; journal = {Proceedings of the International Conference on Machine Learning (ICML)},&#10; year = {2025}&#10;}" role="button">BibTeX</span></p></li> 444<li><p>Habermann, D., Schmitt, M., <strong>Kühmichel, L.</strong>, Bulling, A., Radev, S. T., Bürkner, P. C. (2025). Amortized Bayesian Multilevel Models. <em>Bayesian Analysis</em>. doi:10.1214/25-BA1570 <a href="../publications/pdf/2025__Habermann_et_al__Bayesian_Analysis.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://projecteuclid.org/journals/bayesian-analysis/advance-publication/Amortized-Bayesian-Multilevel-Models/10.1214/25-BA1570.full" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2408.13230" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{habermann2025amortized,&#10; author = {Habermann, D. and Schmitt, M. and Kühmichel, L. and Bulling, A. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Amortized Bayesian Multilevel Models},&#10; journal = {Bayesian Analysis},&#10; year = {2025},&#10; doi = {10.1214/25-BA1570}&#10;}" role="button">BibTeX</span></p></li> 445<li><p>Pogorelyuk, L., Bracher, N. L., Verkleeren, A., <strong>Kühmichel, L.</strong>, Radev, S. T. (2025). Stable Single-Pixel Contrastive Learning for Semantic and Geometric Tasks. <em>NeurIPS Workshop on Unifying Representations in Neural Models</em>. <a href="https://openreview.net/forum?id=nzGuDABwce" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Conference</a> <a href="https://github.com/stefanradev93/oxels" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{Pogorelyuk2025stable,&#10; author = {Pogorelyuk, L. and Bracher, N. L. and Verkleeren, A. and Kühmichel, L. and Radev, S. T.},&#10; title = {Stable Single-Pixel Contrastive Learning for Semantic and Geometric Tasks},&#10; journal = {NeurIPS Workshop on Unifying Representations in Neural Models},&#10; year = {2025}&#10;}" role="button">BibTeX</span></p></li> 446</ul> 447<!-- --> 448</section> 449<section id="abi-applications" class="level2"> 450<h2 class="anchored" data-anchor-id="abi-applications">Applications of Amortized Bayesian Inference</h2> 451<div class="quarto-figure quarto-figure-left"> 452<figure class="figure"> 453<p><img src="../images/mixture_networks_forward.png" class="img-fluid quarto-figure quarto-figure-left figure-img" style="width:80.0%" data-fig-align="left" alt="An illustration of amortized mixture models."></p> 454</figure> 455</div> 456<p>Recent developments in simulation-based amortized inference have ushered in new possibilities for conducting principled Bayesian analysis. The simulation-based approach unlocks the potential of complex models whose likelihoods or priors are not analytically tractable. Amortized approaches make the required computations relatively fast, thus allowing for the deployment of intricate models in scenarios that were hitherto deemed unfeasible or inconvenient. Nevertheless, the novelty of this approach poses a challenge, as its widespread adoption hinges on the availability of user-friendly documentation and resources that simplify entry into the field, as well as empirical examples that validate the methodâs usefulness for the practical researchers.</p> 457<p>In this project, our emphasis is on applications within cognitive modeling and developmental psychology. We focus on how simulation-based amortized inference can address important challenges within the field, not only during the data analysis phase but also in the planning and execution of studies and experiments. As a by-product we will generate tutorials and educational materials providing gentle introductions into the topic. This project also aims to lay the foundations for integrating simulation-based amortized inference with popular statistical software packages used by practitioners who may not have extensive coding skills, thereby broadening the scope of users benefiting from its advantages.</p> 458<p>Overarching Topics: <a href="../research#abi" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Amortized Inference</a> <a href="../research#lvm" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Latent Variable Modeling</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 459<p>Project Members: <a href="../people#simon-kucharsky" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Å imon Kucharský</a></p> 460<p>
460Funders: <a href="https://www.tu-dortmund.de/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">TU Dortmund University</a></p> 461<p>Funding Period: 2024 â 2027</p> 462<p>Publications:</p> 463<ul> 464<li><p><strong>Kucharský, Å .</strong>, Mishra, A., Habermann, D., Radev, S. T., Bürkner, P. C. (in review). Improving the Accuracy of Amortized Model Comparison with Self-Consistency. <em>ArXiv preprint</em>. Short version accepted at <em>NeurIPS Workshop on Reliable Machine Learning from Unreliable Data</em>. <a href="https://arxiv.org/abs/2508.20614" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{kucharsky2026improving,&#10; author = {Kucharský, Å . and Mishra, A. and Habermann, D. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Improving the Accuracy of Amortized Model Comparison with Self-Consistency},&#10; journal = {ArXiv preprint},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 465<li><p>Kühmichel, L., Huang, J. M., Pratz, V., Arruda, J., Olischläger, H., Habermann, D., <strong>Kucharský, Å .</strong>, Elsemüller, L., Mishra, A., Bracher, N., Jedhoff, S., Schmitt, M., Bürkner, P. C., Radev, S. T. (in review). BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2602.07098" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://bayesflow.org/main/index.html" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Software</a> <a href="https://github.com/bayesflow-org/bf2-paper-case-study" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{kuehmichel2026bayesflow,&#10; author = {Kühmichel, L. and Huang, J. M. and Pratz, V. and Arruda, J. and Olischläger, H. and Habermann, D. and Kucharský, Å . and Elsemüller, L. and Mishra, A. and Bracher, N. and Jedhoff, S. and Schmitt, M. and Bürkner, P. C. and Radev, S. T.},&#10; title = {BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python},&#10; journal = {ArXiv preprint},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 466<li><p>Mishra, A., <strong>Kucharský, Å .</strong>, Bürkner, P. C. (in review). Unsupervised Continual Learning for Amortized Bayesian Inference. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2602.22884" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mishra2026CL,&#10; author = {Mishra, A. and Kucharský, Å . and Bürkner, P. C.},&#10; title = {Unsupervised Continual Learning for Amortized Bayesian Inference},&#10; journal = {ArXiv preprint},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 467<li><p><strong>Kucharský, Å .</strong>, Bürkner, P. C. (2026). Amortized Bayesian Mixture Models. <em>Statistics and Computing</em>. doi:10.1007/s11222-026-10911-y <a href="../publications/pdf/2026__Kucharsky_Buerkner__Statistics_and_Computing.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://link.springer.com/article/10.1007/s11222-026-10911-y" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2501.10229" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{kucharsky2026mixture,&#10; author = {Kucharský, Å . and Bürkner, P. C.},&#10; title = {Amortized Bayesian Mixture Models},&#10; journal = {Statistics and Computing},&#10; year = {2026},&#10; doi = {10.1007/s11222-026-10911-y}&#10;}" role="button">BibTeX</span></p></li> 468<li><p><strong>Kucharský, Å .</strong>, Bürkner, P. C. (2025). Amortized Bayesian Cognitive Modeling with BayesFlow. <em>PsyArXiv preprint</em>. doi:10.31234/osf.io/34k6q_v1 <a href="https://osf.io/preprints/psyarxiv/34k6q_v1" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://kucharssim.github.io/bayesflow-cognitive-modeling-book/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Website</a> <a href="https://github.com/Kucharssim/bayesflow-cognitive-modeling-book" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{kucharsky2025amortized,&#10; author = {Kucharský, Å . and Bürkner, P. C.},&#10; title = {Amortized Bayesian Cognitive Modeling with BayesFlow},&#10; journal = {PsyArXiv preprint},&#10; year = {2025},&#10; doi = {10.31234/osf.io/34k6q_v1}&#10;}" role="button">BibTeX</span></p></li> 469</ul> 470<!-- --> 471<p><br> <br></p> 472</section> 473<section id="past-projects" class="level2"> 474<h2 class="anchored" data-anchor-id="past-projects">Past Projects</h2> 475<div class="callout callout-style-default callout-note no-icon callout-titled"> 476<div class="callout-header d-flex align-content-center collapsed" data-bs-toggle="collapse" data-bs-target=".callout-1-contents" aria-controls="callout-1" aria-expanded="false" aria-label="Toggle callout"> 477<div class="callout-icon-container"> 478<i class="callout-icon no-icon"></i> 479</div> 480<div class="callout-title-container flex-fill"> 481<span class="screen-reader-only">Note</span>Amortized Bayesian Inference for Multilevel Models 482</div> 483<div class="callout-btn-toggle d-inline-block border-0 py-1 ps-1 pe-0 float-end"><i class="callout-toggle"></i></div> 484</div> 485<div id="callout-1" class="callout-1-contents callout-collapse collapse"> 486<div class="callout-body-container callout-body"> 487<div class="quarto-figure quarto-figure-left"> 488<figure class="figure"> 489<p><img src="../images/mlm_overview.png" class="img-fluid quarto-figure quarto-figure-left figure-img" alt="An illustration of amortized multilevel models."></p> 490</figure> 491</div> 492<p>Probabilistic multilevel models (MLMs) are a central building block in Bayesian data analysis. Despite their widely acknowledged advantages, MLMs remain challenging to estimate and evaluate, especially when the involved likelihoods or priors are analytically intractable. Recent developments in generative deep learning and simulation-based inference have shown promising results in scaling up Bayesian inference through amortization. However, the utility of deep generative models for learning Bayesian MLMs remains largely unexplored.</p> 493<p>
493In this project, we propose to develop a general and efficient neural inference framework for estimating and evaluating complex Bayesian MLMs. Our framework will substantially extend previous work on simulation-based Bayesian inference for single-level models. Moreover, it aims to encompass not only the inference phase of a Bayesian workflow but also the model evaluation steps, which usually comprise a computational bottleneck with standard (non-amortized) Bayesian methods. Thus, the proposed project has the potential to greatly enhance model-based inference and understanding of complex processes across the quantitative sciences.</p> 494<p>Overarching Topics: <a href="../research#abi" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Amortized Inference</a> <a href="../research#lvm" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Latent Variable Modeling</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 495<p>Project Members: <a href="../people#daniel-habermann" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Daniel Habermann</a></p> 496<p>Funders: <a href="https://www.dfg.de/en/index.jsp" class="btn btn-outline-primary btn-page-header btn-xs" role="button">German Research Foundation (DFG)</a> <a href="https://www.tu-dortmund.de/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">TU Dortmund University</a></p> 497<p>Funding Period: 2023 â 2026</p> 498<p>Publications:</p> 499<ul> 500<li><p>Kucharský, Å ., Mishra, A., <strong>Habermann, D.</strong>, Radev, S. T., Bürkner, P. C. (in review). Improving the Accuracy of Amortized Model Comparison with Self-Consistency. <em>ArXiv preprint</em>. Short version accepted at <em>NeurIPS Workshop on Reliable Machine Learning from Unreliable Data</em>. <a href="https://arxiv.org/abs/2508.20614" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{kucharsky2026improving,&#10; author = {Kucharský, Å . and Mishra, A. and Habermann, D. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Improving the Accuracy of Amortized Model Comparison with Self-Consistency},&#10; journal = {ArXiv preprint},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 501<li><p>Kühmichel, L., Huang, J. M., Pratz, V., Arruda, J., Olischläger, H., <strong>Habermann, D.</strong>, Kucharský, Å ., Elsemüller, L., Mishra, A., Bracher, N., Jedhoff, S., Schmitt, M., Bürkner, P. C., Radev, S. T. (in review). BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2602.07098" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://bayesflow.org/main/index.html" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Software</a> <a href="https://github.com/bayesflow-org/bf2-paper-case-study" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{kuehmichel2026bayesflow,&#10; author = {Kühmichel, L. and Huang, J. M. and Pratz, V. and Arruda, J. and Olischläger, H. and Habermann, D. and Kucharský, Å . and Elsemüller, L. and Mishra, A. and Bracher, N. and Jedhoff, S. and Schmitt, M. and Bürkner, P. C. and Radev, S. T.},&#10; title = {BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python},&#10; journal = {ArXiv preprint},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 502<li><p>Mishra, A., <strong>Habermann, D.</strong>, Schmitt, M., Radev, S. T., Bürkner, P. C. (2026). Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data. <em>International Conference on Learning Representations (ICLR)</em>. <a href="../publications/pdf/2026__Mishra_et_al__ICLR.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://openreview.net/forum?id=RwKyg5BcgN" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2501.13483" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="http://github.com/bayesflow-org/self-consistency-real" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mishra2026robust,&#10; author = {Mishra, A. and Habermann, D. and Schmitt, M. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data},&#10; journal = {International Conference on Learning Representations (ICLR)},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 503<li><p><strong>Habermann, D.</strong>, Schmitt, M., Kühmichel, L., Bulling, A., Radev, S. T., Bürkner, P. C. (2025). Amortized Bayesian Multilevel Models. <em>Bayesian Analysis</em>. doi:10.1214/25-BA1570 <a href="../publications/pdf/2025__Habermann_et_al__Bayesian_Analysis.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://projecteuclid.org/journals/bayesian-analysis/advance-publication/Amortized-Bayesian-Multilevel-Models/10.1214/25-BA1570.full" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2408.13230" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{habermann2025amortized,&#10; author = {Habermann, D. and Schmitt, M. and Kühmichel, L. and Bulling, A. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Amortized Bayesian Multilevel Models},&#10; journal = {Bayesian Analysis},&#10; year = {2025},&#10; doi = {10.1214/25-BA1570}&#10;}" role="button">BibTeX</span></p></li> 504<li><p>Schmitt, M., Ivanova, D. R., <strong>Habermann, D.</strong>, Köthe, U., Bürkner, P. C., Radev, S. T. (2024). Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference. <em>Proceedings of the International Conference on Machine Learning (ICML)</em>. <a href="../publications/pdf/2024__Schmitt_et_al__ICML.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://proceedings.mlr.press/v235/schmitt24a.html" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Conference</a> <a href="https://arxiv.org/abs/2310.04395" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{schmitt2024leveraging,&#10; author = {Schmitt, M. and Ivanova, D. R. and Habermann, D. and Köthe, U. and Bürkner, P. C. and Radev, S. T.},&#10; title = {Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference},&#10; journal = {Proceedings of the International Conference on Machine Learning (ICML)},&#10; year = {2024}&#10;}" role="button">BibTeX</span></p></li> 505</ul> 506</div> 507</div> 508</div> 509<!-- --> 510<div class="callout callout-style-default callout-note no-icon callout-titled"> 511<div class="callout-header d-flex align-content-center collapsed" data-bs-toggle="collapse" data-bs-target=".callout-2-contents" aria-controls="callout-2" aria-expanded="false" aria-label="Toggle callout"> 512<div class="callout-icon-container"> 513<i class="callout-icon no-icon"></i> 514</div> 515<div class="callout-title-container flex-fill"> 516<span class="screen-reader-only">Note</span>Simulation-Based Prior Distributions for Bayesian Models 517</div> 518<div class="callout-btn-toggle d-inline-block border-0 py-1 ps-1 pe-0 float-end"><i class="callout-toggle"></i></div> 519</div> 520<div id="callout-2" class="callout-2-contents callout-collapse collapse"> 521<div class="callout-body-container callout-body"> 522<div class="quarto-figure quarto-figure-left"> 523<figure class="figure"> 524<p><img src="../images/simulation-based-priors.png" class="img-fluid quarto-figure quarto-figure-left figure-img" alt="An illustration of the simulation-based prior workflow."></p> 525</figure> 526</div> 527<p>Data-driven statistical modeling plays a crucial role in almost all quantitative sciences. Despite continuous increases in the amount of available data, the addition of further information sources, such as expert knowledge, often remains an irreplaceable part of setting up high-fidelity models. Grounded in probability theory, Bayesian statistics provides a principled a
527pproach to including expert knowledge in the form of prior distributions, a process called prior elicitation. However, prior elicitation for high-dimensional Bayesian models is infeasible with existing methods due to practical and computational challenges. With the goal of solving these challenges, we propose to develop simulation-based priors for high-dimensional Bayesian models that allow to incorporate prior information elicited on any model-implied quantities. We expect the developed methods to have a major impact on all fields applying probabilistic modeling by making the use of expert knowledge practical, robust, and computationally feasible.</p> 528<p>Overarching Topics: <a href="../research#prior-specification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Prior Specification</a> <a href="../research#abi" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Amortized Inference</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 529<p>Project Members: <a href="https://florence-bockting.github.io" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Florence Bockting</a></p> 530<p>Funders: <a href="https://www.tu-dortmund.de/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">TU Dortmund University</a> <a href="https://www.simtech.uni-stuttgart.de/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Cluster of Excellence SimTech</a></p> 531<p>Funding Period: 2022 â 2025</p> 532<p>Publications:</p> 533<ul> 534<li><p><strong>Bockting, F.</strong>, Bürkner, P. C. (in review). elicito: A Python Package for Expert Prior Elicitation. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2506.16830" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/florence-bockting/elicito" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Software</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{bockting2025elicito,&#10; author = {Bockting, F. and Bürkner, P. C.},&#10; title = {elicito: A Python Package for Expert Prior Elicitation},&#10; journal = {ArXiv preprint},&#10; year = {2025}&#10;}" role="button">BibTeX</span></p></li> 535<li><p><strong>Bockting, F.</strong>, Radev, S. T., Bürkner, P. C. (2025). Expert-elicitation method for non-parametric joint priors using normalizing flows. <em>Statistics and Computing</em>. doi:0.1007/s11222-025-10665-z <a href="../publications/pdf/2025__Bockting_et_al__Statistics_and_Computing.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://link.springer.com/article/10.1007/s11222-025-10665-z" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2411.15826" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/florence-bockting/prior_elicitation/tree/main/elicit/manuscript_non_parametric_joint_prior" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code</a> <a href="https://osf.io/xrzh6/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{bockting2025expert,&#10; author = {Bockting, F. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Expert-elicitation method for non-parametric joint priors using normalizing flows},&#10; journal = {Statistics and Computing},&#10; year = {2025},&#10; doi = {0.1007/s11222-025-10665-z}&#10;}" role="button">BibTeX</span></p></li> 536<li><p><strong>Bockting, F.</strong>, Radev, S. T., Bürkner, P. C. (2024). Simulation-Based Prior Knowledge Elicitation for Parametric Bayesian Models. <em>Scientific Reports</em>. doi:10.1038/s41598-024-68090-7 <a href="../publications/pdf/2024__Bockting_et_al__Scientific_Reports.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://www.nature.com/articles/s41598-024-68090-7" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="http://arxiv.org/abs/2308.11672" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/florence-bockting/PriorLearning" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{bockting2024simulation,&#10; author = {Bockting, F. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Simulation-Based Prior Knowledge Elicitation for Parametric Bayesian Models},&#10; journal = {Scientific Reports},&#10; year = {2024},&#10; doi = {10.1038/s41598-024-68090-7}&#10;}" role="button">BibTeX</span></p></li> 537</ul> 538</div> 539</div> 540</div> 541<!-- --> 542<div class="callout callout-style-default callout-note no-icon callout-titled"> 543<div class="callout-header d-flex align-content-center collapsed" data-bs-toggle="collapse" data-bs-target=".callout-3-contents" aria-controls="callout-3" aria-expanded="false" aria-label="Toggle callout"> 544<div class="callout-icon-container"> 545<i class="callout-icon no-icon"></i> 546</div> 547<div class="callout-title-container flex-fill"> 548<span class="screen-reader-only">Note</span>Bayesian Distributional Latent Variable Models 549</div> 550<div class="callout-btn-toggle d-inline-block border-0 py-1 ps-1 pe-0 float-end"><i class="callout-toggle"></i></div> 551</div> 552<div id="callout-3" class="callout-3-contents callout-collapse collapse"> 553<div class="callout-body-container callout-body"> 554<div class="quarto-figure quarto-figure-left"> 555<figure class="figure"> 556<p><img src="../images/distributional_SEMs.png" class="img-fluid quarto-figure quarto-figure-left figure-img" alt="An illustration of distributional SEMs."></p> 557</figure> 558</div> 559<p>In psychology and related sciences, a lot of research is concerned with studying latent variables, that is, constructs which are not directly observable. Statistical methods for modeling latent variables based on manifest (observable) indicators are thus crucial to the scientific progress in those fields. Two major interconnected statistical areas dealing with latent variables exist, namely, Item Response Theory (I
559RT) and Structural Equation Modeling (SEM). Although the two fields are closely connected, the frontiers of IRT and SEM have developed in somewhat different directions.</p> 560<p>A combination of these two major frontiers would enable researchers to tackle a lot of advanced psychological research questions at the intersection of psychometrics, personnel psychology, cognitive psychology, and applied psychology. In order for us to gain better insights into behavioral and cognitive processes, their mathematical approximations should match the processesâ complexity in both overall distributional form and its components that are expressed as complex functions of predicting variables.</p> 561<p>This project aims to develop a framework for Bayesian distributional latent variable models that combines the principles of IRT and SEM with the flexibility of distributional regression powered by modern Bayesian estimation methods.</p> 562<p>Overarching Topics: <a href="../research#lvm" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Latent Variable Modeling</a> <a href="../research#machine-workflow" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Machine-Assisted Workflows</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 563<p>Project Members: <a href="https://lunafazio.github.io" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Luna Fazio</a></p> 564<p>Funders: <a href="https://www.dfg.de/en/index.jsp" class="btn btn-outline-primary btn-page-header btn-xs" role="button">German Research Foundation (DFG)</a> <a href="https://www.tu-dortmund.de/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">TU Dortmund University</a></p> 565<p>Funding Period: 2022 â 2025</p> 566<p>Publications:</p> 567<ul> 568<li><p><strong>Fazio, L.</strong>, Bürkner, P. C. (in review). Latent Variable Models for Distributional Features. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2606.15526" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/bdlvm-project/dflvm-paper" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{fazio2026latent,&#10; author = {Fazio, L. and Bürkner, P. C.},&#10; title = {Latent Variable Models for Distributional Features},&#10; journal = {ArXiv preprint},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 569<li><p><strong>Fazio, L.</strong>, Scholz, M., Aguilar, J. E., Bürkner, P. C. (in review). Primed Priors for Simulation-Based Validation of Bayesian Models. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2408.06504" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/sims1253/implicit-priors" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{fazio2025primed,&#10; author = {Fazio, L. and Scholz, M. and Aguilar, J. E. and Bürkner, P. C.},&#10; title = {Primed Priors for Simulation-Based Validation of Bayesian Models},&#10; journal = {ArXiv preprint},&#10; year = {2025}&#10;}" role="button">BibTeX</span></p></li> 570<li><p><strong>Fazio, L.</strong>, Bürkner, P. C. (2025). Gaussian distributional structural equation models: A framework for modeling latent heteroscedasticity. <em>Multivariate Behavioral Research</em>. doi:10.1080/00273171.2025.2483252 <a href="../publications/pdf/2025__Fazio_Buerkner__Multivariate_Behavioral_Research.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://www.tandfonline.com/doi/full/10.1080/00273171.2025.2483252" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2404.14124" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/bdlvm-project/gdsem-paper" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{fazio2025gaussian,&#10; author = {Fazio, L. and Bürkner, P. C.},&#10; title = {Gaussian distributional structural equation models: A framework for modeling latent heteroscedasticity},&#10; journal = {Multivariate Behavioral Research},&#10; year = {2025},&#10; doi = {10.1080/00273171.2025.2483252}&#10;}" role="button">BibTeX</span></p></li> 571</ul> 572</div> 573</div> 574</div> 575<!-- --> 576<div class="callout callout-style-default callout-note no-icon callout-titled"> 577<div class="callout-header d-flex align-content-center collapsed" data-bs-toggle="collapse" data-bs-target=".callout-4-contents" aria-controls="callout-4" aria-expanded="false" aria-label="Toggle callout"> 578<div class="callout-icon-container"> 579<i class="callout-icon no-icon"></i> 580</div> 581<div class="callout-title-container flex-fill"> 582<span class="screen-reader-only">Note</span>Probabilistic Models for Single-Cell RNA Sequencing Data 583</div> 584<div class="callout-btn-toggle d-inline-block border-0 py-1 ps-1 pe-0 float-end"><i class="callout-toggle"></i></div> 585</div> 586<div id="callout-4" class="callout-4-contents callout-collapse collapse"> 587<div class="callout-body-container callout-body"> 588<div class="quarto-figure quarto-figure-left"> 589<figure class="figure"> 590<p><img src="../images/latent-derivative-gps.png" class="img-fluid quarto-figure quarto-figure-left figure-img" alt="An illustration of our latent derivative Gaussian process framework."></p> 591</figure> 592</div> 593<p>Trajectory and pseudo-time inference methods in single-cell RNA sequencing face challenges from the ambiguity of the static single-cell transcriptome snapshot data. In this project, we aim to tackle this challenge by means of advanced probabilistic methods. Concretely, we aim to reconstruct unobserved cell ordering as latent pseudo-time by analyzing RNA spliced counts and corresponding derivative RNA velocity. Further, we aim to obtain uncertainty estimates of the latent cell ordering using Bayesian inference. To achieve these goals, we will develop advanced latent Gaussian process models with the ability of utilizing derivative information to increase precision in estimating unobserved latent inputs. This model deploys derivative covariance kernel functions and modifications in the hyperparameter specifications, thu
593s increasing capabilities for utilizing derivative information in a multi-output setting. Although the primary motivation lies in applications in single-cell biology, this model has the potential to solve similar research problems dealing with multi-output data and its derivatives from diverse fields of study.</p> 594<p>Overarching Topics: <a href="../research#lvm" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Latent Variable Modeling</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 595<p>Project Members: <a href="https://www.linkedin.com/in/soham-mukherjee-33a397146" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Soham Mukherjee</a></p> 596<p>Co-Supervisors: <a href="https://claassenlab.github.io/people/manfred-claassen/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Manfred Claassen</a></p> 597<p>Funders: <a href="https://www.tu-dortmund.de/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">TU Dortmund University</a> <a href="https://uni-tuebingen.de/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">University of Tübingen</a></p> 598<p>Funding Period: 2022 â 2025</p> 599<p>Publications:</p> 600<ul> 601<li><p><strong>Mukherjee, S.</strong>, Aguilar, J. E., Zago, M., Claassen, M., Bürkner, P. C. (in review). Latent variable estimation with composite Hilbert space Gaussian processes. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2510.25371" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/Soham6298/Latent-Composite-HSGPs" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mukherjee2025latent,&#10; author = {Mukherjee, S. and Aguilar, J. E. and Zago, M. and Claassen, M. and Bürkner, P. C.},&#10; title = {Latent variable estimation with composite Hilbert space Gaussian processes},&#10; journal = {ArXiv preprint},&#10; year = {2025}&#10;}" role="button">BibTeX</span></p></li> 602<li><p><strong>Mukherjee, S.</strong>, Claassen, M., Bürkner, P. C. (2026). Hilbert space methods for approximating multi-output latent variable Gaussian processes. <em>Statistics and Computing</em>. doi:10.1007/s11222-026-10869-x <a href="../publications/pdf/2026__Mukherjee_et_al__Statistics_and_Computing.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://link.springer.com/article/10.1007/s11222-026-10869-x" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2505.16919" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/Soham6298/Latent-variable-HSGPs" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mukherjee2025hilbert,&#10; author = {Mukherjee, S. and Claassen, M. and Bürkner, P. C.},&#10; title = {Hilbert space methods for approximating multi-output latent variable Gaussian processes},&#10; journal = {Statistics and Computing},&#10; year = {2026},&#10; doi = {10.1007/s11222-026-10869-x}&#10;}" role="button">BibTeX</span></p></li> 603<li><p><strong>Mukherjee, S.</strong>, Claassen, M., Bürkner, P. C. (2025). DGP-LVM: Derivative Gaussian process latent variable models. <em>Statistics and Computing</em>. doi:10.1007/s11222-025-10644-4 <a href="../publications/pdf/2025__Mukherjee_et_al__Statistics_and_Computing.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://link.springer.com/article/10.1007/s11222-025-10644-4" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2404.04074" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/Soham6298/DGP-LVM" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mukherjee2025dgplvm,&#10; author = {Mukherjee, S. and Claassen, M. and Bürkner, P. C.},&#10; title = {DGP-LVM: Derivative Gaussian process latent variable models},&#10; journal = {Statistics and Computing},&#10; year = {2025},&#10; doi = {10.1007/s11222-025-10644-4}&#10;}" role="button">BibTeX</span></p></li> 604</ul> 605</div> 606</div> 607</div> 608<!-- --> 609<div class="callout callout-style-default callout-note no-icon callout-titled"> 610<div class="callout-header d-flex align-content-center collapsed" data-bs-toggle="collapse" data-bs-target=".callout-5-contents" aria-controls="callout-5" aria-expanded="false" aria-label="Toggle callout"> 611<div class="callout-icon-container"> 612<i class="callout-icon no-icon"></i> 613</div> 614<div class="callout-title-container flex-fill"> 615<span class="screen-reader-only">Note</span>Data-Integrated Training of Surrogate Models for Uncertainty Quantification 616</div> 617<div class="callout-btn-toggle d-inline-block border-0 py-1 ps-1 pe-0 float-end"><i class="callout-toggle"></i></div> 618</div> 619<div id="callout-5" class="callout-5-contents callout-collapse collapse"> 620<div class="callout-body-container callout-body"> 621<div class="quarto-figure quarto-figure-left"> 622<figure class="figure"> 623<p><img src="../images/uncertainty_prop_workflow.png" class="img-fluid quarto-figure quarto-figure-left figure-img" style="width:80.0%" alt="Surrogate uncertainty propagation workflow."></p> 624</figure> 625</div> 626<p>Uncertainty quantification is crucial to assess the predictive power and limitations of complex systems models. However, in the case of high-dimensional parameter spaces and/or complex functional relationships, physics-based simulation models are often computationally too demanding for rigorous Bayesian uncertainty quantification. Surrogate models allow for such analyses with much lower effort. They are typically trained such that they fit the simulation reference best.</p> 627<p>What is left unexplored is the possibility of surrogate models to actually fit observed data better than the reference model. This phenomenon occurs when structural misspecification of the physics-constrained reference model limits its performance, but at the same time, the more flexible data-driven surrogate model can better capture the relation of output and input data. Such situations offer huge potential for diagnostic evaluation of the modelling approach toward deeper system understanding and model improvement.</p> 628<p>We aim at developing (1) a weighted data-integrated surrogate training approach for improved predictive performance, (2) a diagnostic approach for structural error detection in the reference model, and (3) an uncertainty propagation analysis that accounts for the approximation error introduced by the use of surrogates.</p> 629<p>Overarching Topics: <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 630<p>Project Members: <a href="https://de.linkedin.com/in/philipp-reiser-a33163165" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Philipp Reiser</a></p> 631<p>Co-Supervisors: <a href="https://www.simtech.uni-stuttgart.de/exc/people/Guthke/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Anneli Guthke</a></p> 632<p>Funders: <a href="https://www.simtech.uni-stuttgart.de/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Cluster of Excellence SimTech</a></p> 633<p>
633Funding Period: 2022 â 2025</p> 634<p>Publications:</p> 635<ul> 636<li><p><strong>Reiser, P.</strong>, Bürkner, P. C., Guthke, A. (2026). Bayesian Surrogate Training on Multiple Data Sources: A Hybrid Modeling Strategy. <em>Statistics and Computing</em>. doi:10.1007/s11222-026-10906-9 <a href="../publications/pdf/2026__Reiser_et_al__Statistics_and_Computing.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://doi.org/10.1007/s11222-026-10906-9" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2412.11875" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/philippreiser/multi-data-source-bayesian-surrogate-paper" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{reiser2026bayesian,&#10; author = {Reiser, P. and Bürkner, P. C. and Guthke, A.},&#10; title = {Bayesian Surrogate Training on Multiple Data Sources: A Hybrid Modeling Strategy},&#10; journal = {Statistics and Computing},&#10; year = {2026},&#10; doi = {10.1007/s11222-026-10906-9}&#10;}" role="button">BibTeX</span></p></li> 637<li><p>Scheurer, S., <strong>Reiser, P.</strong>, Brünnette, T., Nowak, W., Guthke, A., Bürkner, P. C. (2026). Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models. <em>Transactions in Machine Learning Research</em>. <a href="../publications/pdf/2026__Scheurer_et_al__TMLR.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://openreview.net/forum?id=aVSoQXbfy1" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2505.08683" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/LS3-university-of-stuttgart/ua-sabi-paper" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{scheurer2026uncertainty,&#10; author = {Scheurer, S. and Reiser, P. and Brünnette, T. and Nowak, W. and Guthke, A. and Bürkner, P. C.},&#10; title = {Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models},&#10; journal = {Transactions in Machine Learning Research},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 638<li><p><strong>Reiser, P.</strong>, Aguilar, J. E., Guthke, A., Bürkner, P. C. (2025). Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference. <em>Statistics and Computing</em>. doi:10.1007/s11222-025-10597-8 <a href="../publications/pdf/2025__Reiser_et_al__Statistics_and_Computing.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://link.springer.com/article/10.1007/s11222-025-10597-8" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2312.05153" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/philippreiser/bayesian-surrogate-uncertainty-paper" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{reiser2025uncertainty,&#10; author = {Reiser, P. and Aguilar, J. E. and Guthke, A. and Bürkner, P. C.},&#10; title = {Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference},&#10; journal = {Statistics and Computing},&#10; year = {2025},&#10; doi = {10.1007/s11222-025-10597-8}&#10;}" role="button">BibTeX</span></p></li> 639</ul> 640</div> 641</div> 642</div> 643<!-- --> 644<div class="callout callout-style-default callout-note no-icon callout-titled"> 645<div class="callout-header d-flex align-content-center collapsed" data-bs-toggle="collapse" data-bs-target=".callout-6-contents" aria-controls="callout-6" aria-expanded="false" aria-label="Toggle callout"> 646<div class="callout-icon-container"> 647<i class="callout-icon no-icon"></i> 648</div> 649<div class="callout-title-container flex-fill"> 650<span class="screen-reader-only">Note</span>Meta-Uncertainty in Bayesian Model Comparison 651</div> 652<div class="callout-btn-toggle d-inline-block border-0 py-1 ps-1 pe-0 float-end"><i class="callout-toggle"></i></div> 653</div> 654<div id="callout-6" class="callout-6-contents callout-collapse collapse"> 655<div class="callout-body-container callout-body"> 656<p><img src="../images/meta_uncertainty_banner.png" class="img-fluid" alt="An illustration of meta-uncertainty."></p> 657<p>What we can learn from a single data set in experiments and observational studies is always limited, and we are inevitably left with some remaining uncertainty. It is of utmost importance to take this uncertainty into account when drawing conclusions if we want to make real scientific progress. Formalizing and quantifying uncertainty is thus at the heart of statistical methods aiming to obtain insights from data.</p> 658<p>To compare scientific theories, scientists translate them into statistical models and then investigate how well the modelsâ predictions match the gathered real-world data. One widely applied approach to compare statistical models is Bayesian model comparison (BMC). Relying on BMC, researchers obtain the probability that each of the competing models is true (or is closest to the truth) given the data. These probabilities are measures of uncertainty and, yet, are also uncertain themselves. This is what we call meta-uncertainty (uncertainty over uncertainties). Meta-uncertainty affects the conclusions we can draw from model comparisons and, consequently, the conclusions we can draw about the underlying scientific theories.</p> 659<p>This project contributes to this endeavor by developing and evaluating methods for quantifying meta-uncertainty in BMC. Building upon mathematical theory of meta-uncertainty, we will utilize extensive model simulations as an additional source of information, which enable us to quantify so-far implicit yet important assumptions of BMC. What is more, we will be able to differentiate between a closed world, where the true model is assumed to be within the set of considered models, and an open world, where the true model may not be within that set â a critical distinction in the context of model comparison procedures.</p> 660<p>Overarching Topics: <a href="../research#model-comparison" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Model Comparison</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a> <a href="../research#abi" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Amortized Inference</a></p> 661<p>Project Members: <a href="https://marvin-schmitt.com//" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Marvin Schmitt</a></p> 662<p>Funders: <a href="https://cyber-valley.de/en/research-fund" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Cyber Valley Research Fund</a></p> 663<p>
663Funding Period: 2021 â 2025</p> 664<p>Publications:</p> 665<ul> 666<li><p>Li, C., Vehtari, A., Bürkner, P. C., Radev, S. T., Acerbi, L., <strong>Schmitt, M.</strong> (2026). Amortized Bayesian Workflow. <em>Transactions in Machine Learning Research</em>. <a href="../publications/pdf/2026__Li_et_al__TMLR.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://openreview.net/forum?id=osV7adJlKD" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2409.04332" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/pipme/amortized-Bayesian-workflow" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{li2025amortized,&#10; author = {Li, C. and Vehtari, A. and Bürkner, P. C. and Radev, S. T. and Acerbi, L. and Schmitt, M.},&#10; title = {Amortized Bayesian Workflow},&#10; journal = {Transactions in Machine Learning Research},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 667<li><p>Mishra, A., Habermann, D., <strong>Schmitt, M.</strong>, Radev, S. T., Bürkner, P. C. (2026). Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data. <em>International Conference on Learning Representations (ICLR)</em>. <a href="../publications/pdf/2026__Mishra_et_al__ICLR.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://openreview.net/forum?id=RwKyg5BcgN" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2501.13483" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="http://github.com/bayesflow-org/self-consistency-real" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mishra2026robust,&#10; author = {Mishra, A. and Habermann, D. and Schmitt, M. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data},&#10; journal = {International Conference on Learning Representations (ICLR)},&#10; year = {2026}&#10;}" role="button">BibTeX</span></p></li> 668<li><p>Säilynoja, T., <strong>Schmitt, M.</strong>, Bürkner, P. C., Vehtari, A. (2026). Posterior SBC: Simulation-Based Calibration Checking Conditional on Data. <em>Statistics and Computing</em>. doi:10.1007/s11222-026-10825-9 <a href="../publications/pdf/2026__Sailynoja_et_al__Statistics_and_Computing.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://link.springer.com/article/10.1007/s11222-026-10825-9" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2502.03279" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/TeemuSailynoja/posterior-sbc" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{sailynoja2026posterior,&#10; author = {Säilynoja, T. and Schmitt, M. and Bürkner, P. C. and Vehtari, A.},&#10; title = {Posterior SBC: Simulation-Based Calibration Checking Conditional on Data},&#10; journal = {Statistics and Computing},&#10; year = {2026},&#10; doi = {10.1007/s11222-026-10825-9}&#10;}" role="button">BibTeX</span></p></li> 669<li><p>Habermann, D., <strong>Schmitt, M.</strong>, Kühmichel, L., Bulling, A., Radev, S. T., Bürkner, P. C. (2025). Amortized Bayesian Multilevel Models. <em>Bayesian Analysis</em>. doi:10.1214/25-BA1570 <a href="../publications/pdf/2025__Habermann_et_al__Bayesian_Analysis.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://projecteuclid.org/journals/bayesian-analysis/advance-publication/Amortized-Bayesian-Multilevel-Models/10.1214/25-BA1570.full" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2408.13230" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{habermann2025amortized,&#10; author = {Habermann, D. and Schmitt, M. and Kühmichel, L. and Bulling, A. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Amortized Bayesian Multilevel Models},&#10; journal = {Bayesian Analysis},&#10; year = {2025},&#10; doi = {10.1214/25-BA1570}&#10;}" role="button">BibTeX</span></p></li> 670<li><p>Elsemüller, L., Olischläger, H., <strong>Schmitt, M.</strong>, Bürkner, P. C., Köthe, U., Radev, S. T. (2024). Sensitivity-Aware Amortized Bayesian Inference. <em>Transactions in Machine Learning Research</em>. <a href="../publications/pdf/2024__Elsemueller_et_al__TMLR.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://openreview.net/forum?id=Kxtpa9rvM0" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2310.11122" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/bayesflow-org/SA-ABI" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{elsemueller2024sensitivity,&#10; author = {Elsemüller, L. and Olischläger, H. and Schmitt, M. and Bürkner, P. C. and Köthe, U. and Radev, S. T.},&#10; title = {Sensitivity-Aware Amortized Bayesian Inference},&#10; journal = {Transactions in Machine Learning Research},&#10; year = {2024}&#10;}" role="button">BibTeX</span></p></li> 671<li><p><strong>Schmitt, M.</strong>, Hikida, Y., Radev, S. T., Sadlo, F., Bürkner, P. C. (2024). The Simplex Projection: Lossless Visualization of 4D Compositional Data on a 2D Canvas. <em>ArXiv preprint</em>. doi:10.48550/arXiv.2403.11141 <a href="../publications/pdf/2024__Schmitt_et_al__arXiv_b.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://arxiv.org/abs/2403.11141" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/marvinschmitt/ggsimplex" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Software</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{schmitt2024simplex,&#10; author = {Schmitt, M. and Hikida, Y. and Radev, S. T. and Sadlo, F. and Bürkner, P. C.},&#10; title = {The Simplex Projection: Lossless Visualization of 4D Compositional Data on a 2D Canvas},&#10; journal = {ArXiv preprint},&#10; year = {2024},&#10; doi = {10.48550/arXiv.2403.11141}&#10;}" role="button">BibTeX</span></p></li> 672<li><p><strong>Schmitt, M.</strong>, Bürkner, P. C., Köthe, U., Radev, S. T. (2024). Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigation. <em>ArXiv preprint</em>. doi:10.48550/arXiv.2406.03154 <a href="../publications/pdf/2024__Schmitt_et_al__arXiv_c.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://arxiv.org/abs/2406.03154" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/marvinschmitt/ModelMisspecificationBF" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{schmitt2025detecting,&#10; author = {Schmitt, M. and Bürkner, P. C. and Köthe, U. and Radev, S. T.},&#10; title = {Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigation},&#10; journal = {ArXiv preprint},&#10; year = {2024},&#10; doi = {10.48550/arXiv.2406.03154}&#10;}" role="button">BibTeX</span></p></li> 673<li><p><strong>Schmitt, M.</strong>
673, Pratz, V., Köthe, U., Bürkner, P. C., Radev, S. T. (2024). Consistency Models for Scalable and Fast Simulation-Based Inference. <em>Proceedings of the Conference on Neural Information Processing Systems (NeurIPS)</em>. <a href="../publications/pdf/2024__Schmitt_et_al__NeurIPS.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://proceedings.neurips.cc/paper_files/paper/2024/hash/e58026e2b2929108e1bd24cbfa1c8e4b-Abstract-Conference.html" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Conference</a> <a href="https://arxiv.org/abs/2312.05440" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{schmitt2024consistency,&#10; author = {Schmitt, M. and Pratz, V. and Köthe, U. and Bürkner, P. C. and Radev, S. T.},&#10; title = {Consistency Models for Scalable and Fast Simulation-Based Inference},&#10; journal = {Proceedings of the Conference on Neural Information Processing Systems (NeurIPS)},&#10; year = {2024}&#10;}" role="button">BibTeX</span></p></li> 674<li><p><strong>Schmitt, M.</strong>, Ivanova, D. R., Habermann, D., Köthe, U., Bürkner, P. C., Radev, S. T. (2024). Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference. <em>Proceedings of the International Conference on Machine Learning (ICML)</em>. <a href="../publications/pdf/2024__Schmitt_et_al__ICML.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://proceedings.mlr.press/v235/schmitt24a.html" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Conference</a> <a href="https://arxiv.org/abs/2310.04395" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{schmitt2024leveraging,&#10; author = {Schmitt, M. and Ivanova, D. R. and Habermann, D. and Köthe, U. and Bürkner, P. C. and Radev, S. T.},&#10; title = {Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference},&#10; journal = {Proceedings of the International Conference on Machine Learning (ICML)},&#10; year = {2024}&#10;}" role="button">BibTeX</span></p></li> 675<li><p><strong>Schmitt, M.</strong>, Radev, S. T., Bürkner, P. C. (2024). Fuse It or Lose It: Deep Fusion for Multimodal Simulation-Based Inference. <em>ArXiv preprint</em>. doi:10.48550/arXiv.2311.10671 <a href="../publications/pdf/2024__Schmitt_et_al__arXiv.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://arxiv.org/abs/2311.10671" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{schmitt2024fuse,&#10; author = {Schmitt, M. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Fuse It or Lose It: Deep Fusion for Multimodal Simulation-Based Inference},&#10; journal = {ArXiv preprint},&#10; year = {2024},&#10; doi = {10.48550/arXiv.2311.10671}&#10;}" role="button">BibTeX</span></p></li> 676<li><p>Radev, S. T., <strong>Schmitt, M.</strong>, Pratz, V., Picchini, U., Köthe, U., Bürkner, P. C. (2023). JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models. <em>Uncertainty in Artificial Intelligence (UAI) Conference Proceedings</em>. <a href="../publications/pdf/2023__Radev_et_al__UAI.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://proceedings.mlr.press/v216/radev23a.html" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Conference</a> <a href="https://arxiv.org/abs/2302.09125" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/bayesflow-org/JANA-Paper" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <a href="../talks/pdf/glimpse_amortized_bayesian_inference.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Talk</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{radev2023jana,&#10; author = {Radev, S. T. and Schmitt, M. and Pratz, V. and Picchini, U. and Köthe, U. and Bürkner, P. C.},&#10; title = {JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models},&#10; journal = {Uncertainty in Artificial Intelligence (UAI) Conference Proceedings},&#10; year = {2023}&#10;}" role="button">BibTeX</span></p></li> 677<li><p>Radev, S. T., <strong>Schmitt, M.</strong>, Schumacher, L., Elsemüller, L., Pratz, V., Schälte, Y., Köthe, U., Bürkner, P. C. (2023). BayesFlow: Amortized Bayesian Workflows With Neural Networks. <em>Journal of Open Source Software</em>. doi:10.21105/joss.05702 <a href="../publications/pdf/2023__Radev_et_al__JOSS.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://joss.theoj.org/papers/10.21105/joss.05702" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2306.16015" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="../software#bayesflow" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Software</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{radev2023bayesflow,&#10; author = {Radev, S. T. and Schmitt, M. and Schumacher, L. and Elsemüller, L. and Pratz, V. and SchÃ
677¤lte, Y. and Köthe, U. and Bürkner, P. C.},&#10; title = {BayesFlow: Amortized Bayesian Workflows With Neural Networks},&#10; journal = {Journal of Open Source Software},&#10; year = {2023},&#10; doi = {10.21105/joss.05702}&#10;}" role="button">BibTeX</span></p></li> 678<li><p><strong>Schmitt, M.</strong>, Radev, S. T., Bürkner, P. C. (2023). Meta-Uncertainty in Bayesian Model Comparison. <em>Artificial Intelligence and Statistics (AISTATS) Conference Proceedings</em>. <a href="../publications/pdf/2023__Schmitt_et_al__AISTATS.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://proceedings.mlr.press/v206/schmitt23a.html" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Conference</a> <a href="http://arxiv.org/abs/2210.07278" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/marvinschmitt/MetaUncertaintyPaper" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <a href="../talks/pdf/poster_meta_uncertainty.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Talk</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{schmitt2023meta,&#10; author = {Schmitt, M. and Radev, S. T. and Bürkner, P. C.},&#10; title = {Meta-Uncertainty in Bayesian Model Comparison},&#10; journal = {Artificial Intelligence and Statistics (AISTATS) Conference Proceedings},&#10; year = {2023}&#10;}" role="button">BibTeX</span></p></li> 679<li><p><strong>Schmitt, M.</strong>, Bürkner, P. C., Köthe, U., Radev, S. T. (2023). Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks. <em>Proceedings of the German Conference on Pattern Recognition (GCPR)</em>. doi:10.1007/978-3-031-54605-1_35 <a href="../publications/pdf/2023__Schmitt_et_al__GCPR.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://link.springer.com/chapter/10.1007/978-3-031-54605-1_35" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2112.08866" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/marvinschmitt/ModelMisspecificationBF" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <a href="../talks/pdf/detecting_MMS_bayesflow.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Talk</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{schmitt2023detecting,&#10; author = {Schmitt, M. and Bürkner, P. C. and Köthe, U. and Radev, S. T.},&#10; title = {Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks},&#10; journal = {Proceedings of the German Conference on Pattern Recognition (GCPR)},&#10; year = {2023},&#10; doi = {10.1007/978-3-031-54605-1_35}&#10;}" role="button">BibTeX</span></p></li> 680</ul> 681<p>Software:</p> 682<ul> 683<li>ggsimplex: Simplex visualizations with ggplot2 <a href="https://github.com/marvinschmitt/ggsimplex" class="btn btn-outline-primary btn-page-header btn-xs" role="button">GitHub</a></li> 684</ul> 685</div> 686</div> 687</div> 688<!-- --> 689<div class="callout callout-style-default callout-note no-icon callout-titled"> 690<div class="callout-header d-flex align-content-center collapsed" data-bs-toggle="collapse" data-bs-target=".callout-7-contents" aria-controls="callout-7" aria-expanded="false" aria-label="Toggle callout"> 691<div class="callout-icon-container"> 692<i class="callout-icon no-icon"></i> 693</div> 694<div class="callout-title-container flex-fill"> 695<span class="screen-reader-only">Note</span>Intuitive Joint Priors for Bayesian Multilevel Models 696</div> 697<div class="callout-btn-toggle d-inline-block border-0 py-1 ps-1 pe-0 float-end"><i class="callout-toggle"></i></div> 698</div> 699<div id="callout-7" class="callout-7-contents callout-collapse collapse"> 700<div class="callout-body-container callout-body"> 701<p><img src="../images/coef_r2d2_marginal.png" class="img-fluid" alt="Marginal densities of the R2D2 prior's coefficients."></p> 702<p>Regression models are ubiquitous in the quantitative sciences making up a big part of all statistical analysis performed on data. In the quantitative sciences, data often contains multilevel structure, for example, because of natural groupings of individuals or repeated measurement of the same individuals. Multilevel models (MLMs) are designed specifically to account for the nested structure in multilevel data and are a widely applied class of regression models. From a Bayesian perspective, the widespread success of MLMs can be explained by the fact that they impose joint priors over a set of parameters with shared hyper-parameters, rather than separate independent priors for each parameter. However, in almost all state-of-the-art approaches, different additive regression terms in MLMs, corresponding to different parameter sets, still receive mutually independent priors. As more and more terms are being added to the model while the number of observations remains constant, such models will overfit the data. This is highly problematic as it leads to unreliable or uninterpretable estimates, bad out-of-sample predictions, and inflated Type I error rates.</p> 703<p>To solve these challenges, this project aims to develop, evaluate, implement, and apply intuitive joint priors for Bayesian MLMs. We hypothesize that our developed priors will enable the reliable and interpretable estimation of much more complex Bayesian MLMs than was previously possible.</p> 704<p>Overarching Topics: <a href="../research#prior-specification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Prior Specification</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 705<p>Project Members: <a href="https://jear2412.github.io" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Javier Aguilar</a></p> 706<p>
706Funders: <a href="https://www.dfg.de/en/index.jsp" class="btn btn-outline-primary btn-page-header btn-xs" role="button">German Research Foundation (DFG)</a> <a href="https://www.tu-dortmund.de/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">TU Dortmund University</a> <a href="https://www.uni-stuttgart.de/en/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">University of Stuttgart</a></p> 707<p>Funding Period: 2021 â 2026</p> 708<p>Publications:</p> 709<ul> 710<li><p><strong>Aguilar, J. E.</strong>, Bürkner, P. C. (in review). Dependency-Aware Shrinkage Priors for High Dimensional Regression. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2505.10715" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://osf.io/fuean/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{aguilar2025dependency,&#10; author = {Aguilar, J. E. and Bürkner, P. C.},&#10; title = {Dependency-Aware Shrinkage Priors for High Dimensional Regression},&#10; journal = {ArXiv preprint},&#10; year = {2025}&#10;}" role="button">BibTeX</span></p></li> 711<li><p><strong>Aguilar, J. E.</strong>, Kohns, D., Vehtari, A., Bürkner, P. C. (in review). R2 priors for Grouped Variance Decomposition in High-dimensional Regression. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2507.11833" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/jear2412/GroupR2priors" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{aguilar2025r2priors,&#10; author = {Aguilar, J. E. and Kohns, D. and Vehtari, A. and Bürkner, P. C.},&#10; title = {R2 priors for Grouped Variance Decomposition in High-dimensional Regression},&#10; journal = {ArXiv preprint},&#10; year = {2025}&#10;}" role="button">BibTeX</span></p></li> 712<li><p>Fazio, L., Scholz, M., <strong>Aguilar, J. E.</strong>, Bürkner, P. C. (in review). Primed Priors for Simulation-Based Validation of Bayesian Models. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2408.06504" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/sims1253/implicit-priors" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{fazio2025primed,&#10; author = {Fazio, L. and Scholz, M. and Aguilar, J. E. and Bürkner, P. C.},&#10; title = {Primed Priors for Simulation-Based Validation of Bayesian Models},&#10; journal = {ArXiv preprint},&#10; year = {2025}&#10;}" role="button">BibTeX</span></p></li> 713<li><p>Mukherjee, S., <strong>Aguilar, J. E.</strong>, Zago, M., Claassen, M., Bürkner, P. C. (in review). Latent variable estimation with composite Hilbert space Gaussian processes. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2510.25371" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/Soham6298/Latent-Composite-HSGPs" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mukherjee2025latent,&#10; author = {Mukherjee, S. and Aguilar, J. E. and Zago, M. and Claassen, M. and Bürkner, P. C.},&#10; title = {Latent variable estimation with composite Hilbert space Gaussian processes},&#10; journal = {ArXiv preprint},&#10; year = {2025}&#10;}" role="button">BibTeX</span></p></li> 714<li><p><strong>Aguilar, J. E.</strong>, Bürkner, P. C. (2025). Generalized Decomposition Priors on R2. <em>Bayesian Analysis</em>. doi:10.1214/25-BA1524 <a href="../publications/pdf/2025__Aguilar_Buerkner__Bayesian_Analysis.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://projecteuclid.org/journals/bayesian-analysis/advance-publication/Generalized-Decomposition-Priors-on-R2/10.1214/25-BA1524.full" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2401.10180" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://osf.io/ns2cv/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{aguilar2025generalized,&#10; author = {Aguilar, J. E. and Bürkner, P. C.},&#10; title = {Generalized Decomposition Priors on R2},&#10; journal = {Bayesian Analysis},&#10; year = {2025},&#10; doi = {10.1214/25-BA1524}&#10;}" role="button">BibTeX</span></p></li> 715<li><p>Reiser, P., <strong>Aguilar, J. E.</strong>, Guthke, A., Bürkner, P. C. (2025). Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference. <em>Statistics and Computing</em>. doi:10.1007/s11222-025-10597-8 <a href="../publications/pdf/2025__Reiser_et_al__Statistics_and_Computing.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://link.springer.com/article/10.1007/s11222-025-10597-8" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2312.05153" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/philippreiser/bayesian-surrogate-uncertainty-paper" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{reiser2025uncertainty,&#10; author = {Reiser, P. and Aguilar, J. E. and Guthke, A. and Bürkner, P. C.},&#10; title = {Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference},&#10; journal = {Statistics and Computing},&#10; year = {2025},&#10; doi = {10.1007/s11222-025-10597-8}&#10;}" role="button">BibTeX</span></p></li> 716<li><p><strong>Aguilar, J. E.</strong>, Bürkner, P. C. (2023). Intuitive Joint Priors for Bayesian Linear Multilevel Models: The R2D2M2 prior. <em>Electronic Journal of Statistics</em>. doi:10.1214/23-EJS2136 <a href="../publications/pdf/2023__Aguilar_Buerkner__Electronic_Journal_of_Statistics.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://doi.org/10.1214/23-EJS2136" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2208.07132" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://osf.io/wgsth/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <a href="../talks/pdf/poster_R2D2M2_prior.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Talk</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{aguilar2023intuitive,&#10; author = {Aguilar, J. E. and Bürkner, P. C.},&#10; title = {Intuitive Joint Priors for Bayesian Linear Multilevel Models: The R2D2M2 prior},&#10; journal = {Electronic Journal of Statistics},&#10; year = {2023},&#10; doi = {10.1214/23-EJS2136}&#10;}" role="button">BibTeX</span></p></li> 717</ul> 718</div> 719</div> 720</div> 721<!-- --> 722<div class="callout callout-style-default callout-note no-icon callout-titled"> 723<div class="callout-header d-flex align-content-center collapsed" data-bs-toggle="collapse" data-bs-target=".callout-8-contents" aria-controls="callout-8" aria-expanded="false" aria-label="Toggle callout"> 724<div class="callout-icon-container"> 725<i class="callout-icon no-icon"></i> 726</div> 727<div class="callout-title-container flex-fill"> 728<span class="screen-reader-only">Note</span>Machine Learning for Bayesian Model Building 729</div> 730<div class="callout-btn-toggle d-inline-block border-0 py-1 ps-1 pe-0 float-end"><i class="callout-toggle"></i></div> 731</div> 732<div id="callout-8" class="callout-8-contents callout-collapse collapse"> 733<div class="callout-body-container callout-body"> 734<div class="quarto-figure quarto-figure-left"> 735<figure class="figure"> 736<p><img src="../images/pad-model-taxonomy.png" class="img-fluid quarto-figure quarto-figure-left figure-img" style="width:80.0%" alt="An illustration of the PAD model taxonomy."></p> 737</figure> 738</div> 739<p>The Bayesian approach to data analysis provides a consistent and flexible way to handle uncertainty in all observations, model parameters, and model structure using probability theory. However, building Bayesian models in a principled way remains a highly complex task requiring a lot of expertise and cognitive resources. In this project, we will develop a machine assisted workflow for building interpretable, robust, and well-predicting Bayesian models. Based on statistical theory, we will develop a framework for simulating realistic data with known modeling challenges. Subsequently, using neural network architectures tuned to the structure of the fitted Bayesian models, machines will be trained on the simulated data to provide automatic model evaluation and modeling recommendations that guide the user through the model building process using interactive visualizations. While leaving the modeling choices up to the user, the machine learns from the userâs decisions to improve its recommendations on the fly.</p> 740<p>Overarching Topics: <a href="../research#machine-workflow" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Machine-Assisted Workflows</a> <a href="../research#model-comparison" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Model Comparison</a> <a href="../research#uncertainty-quantification" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Uncertainty Quantification</a></p> 741<p>Project Members: <a href="https://www.scholzmx.com/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">
741Maximilian Scholz</a></p> 742<p>Funders: <a href="https://www.simtech.uni-stuttgart.de/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Cluster of Excellence SimTech</a></p> 743<p>Funding Period: 2021 â 2024</p> 744<p>Publications:</p> 745<ul> 746<li><p>Fazio, L., <strong>Scholz, M.</strong>, Aguilar, J. E., Bürkner, P. C. (in review). Primed Priors for Simulation-Based Validation of Bayesian Models. <em>ArXiv preprint</em>. <a href="https://arxiv.org/abs/2408.06504" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/sims1253/implicit-priors" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{fazio2025primed,&#10; author = {Fazio, L. and Scholz, M. and Aguilar, J. E. and Bürkner, P. C.},&#10; title = {Primed Priors for Simulation-Based Validation of Bayesian Models},&#10; journal = {ArXiv preprint},&#10; year = {2025}&#10;}" role="button">BibTeX</span></p></li> 747<li><p><strong>Scholz, M.</strong>, Bürkner, P. C. (2025). Prediction can be safely used as a proxy for explanation in causally consistent Bayesian generalized linear models. <em>Journal of Statistical Computation and Simulation</em>. doi:10.1080/00949655.2024.2449534 <a href="../publications/pdf/2025__Scholz_Buerkner__Journal_of_Statistical_Computation_and_Simulation.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://www.tandfonline.com/doi/full/10.1080/00949655.2024.2449534" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="https://arxiv.org/abs/2210.06927" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/sims1253/bayesim" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Software</a> <a href="https://osf.io/xgkzv/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{scholz2025prediction,&#10; author = {Scholz, M. and Bürkner, P. C.},&#10; title = {Prediction can be safely used as a proxy for explanation in causally consistent Bayesian generalized linear models},&#10; journal = {Journal of Statistical Computation and Simulation},&#10; year = {2025},&#10; doi = {10.1080/00949655.2024.2449534}&#10;}" role="button">BibTeX</span></p></li> 748<li><p>Bürkner, P. C., <strong>Scholz, M.</strong>, Radev, S. T. (2023). Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy. <em>Statistics Surveys</em>. doi:10.1214/23-SS145 <a href="../publications/pdf/2023__Buerkner_et_al__Statistics_Surveys.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://doi.org/10.1214/23-SS145" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Journal</a> <a href="http://arxiv.org/abs/2209.02439" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{buerkner2023some,&#10; author = {Bürkner, P. C. and Scholz, M. and Radev, S. T.},&#10; title = {Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy},&#10; journal = {Statistics Surveys},&#10; year = {2023},&#10; doi = {10.1214/23-SS145}&#10;}" role="button">BibTeX</span></p></li> 749<li><p><strong>Scholz, M.</strong>, Bürkner, P. C. (2023). Posterior accuracy and calibration under misspecification in Bayesian generalized linear models. <em>ArXiv preprint</em>. doi:10.48550/arXiv.2311.09081 <a href="../publications/pdf/2023__Scholz_Buerkner__ArXiv.pdf" class="btn btn-outline-primary btn-page-header btn-xs" role="button">PDF</a> <a href="https://arxiv.org/abs/2311.09081" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Preprint</a> <a href="https://github.com/sims1253/bayesim" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Software</a> <a href="https://osf.io/tmdcf/" class="btn btn-outline-primary btn-page-header btn-xs" role="button">Code & Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{scholz2023posterior,&#10; author = {Scholz, M. and Bürkner, P. C.},&#10; title = {Posterior accuracy and calibration under misspecification in Bayesian generalized linear models},&#10; journal = {ArXiv preprint},&#10; year = {2023},&#10; doi = {10.48550/arXiv.2311.09081}&#10;}" role="button">BibTeX</span></p></li> 750</ul> 751<p>Software:</p> 752<ul> 753<li>bayesim: Simulations for Bayesian models <a href="https://github.com/sims1253/bayesim" class="btn btn-outline-primary btn-page-header btn-xs" role="button">GitHub</a></li> 754<li>bayeshear: Metrics for evaluating Bayesian models <a href="https://github.com/sims1253/bayeshear" class="btn btn-outline-primary btn-page-header btn-xs" role="button">GitHub</a></li> 755<li>bayesfam: Custom families for brms <a href="https://github.com/sims1253/bayesfam" class="btn btn-outline-primary btn-page-header btn-xs" role="button">GitHub</a></li> 756</ul> 757</div> 758</div> 759</div> 760 761 762</section> 763 764</main> <!-- /main -->
765<script> 766document.addEventListener("DOMContentLoaded", function () { 767 768 function decodeHtml(html) { 769 const txt = document.createElement("textarea"); 770 txt.innerHTML = html; 771 return txt.value; 772 } 773 774 document.querySelectorAll('[data-bibtex]').forEach(btn => { 775 btn.addEventListener('click', function () { 776 777 let text = this.getAttribute('data-bibtex'); 778 text = decodeHtml(text); 779 780 // Normalize indentation: 2 spaces for all inner lines 781 const lines = text.split("\n"); 782 783 const formatted = lines.map((line, i) => { 784 if (i === 0 || line.trim() === "}") return line.trim(); 785 return " " + line.trim(); 786 }).join("\n"); 787 788 navigator.clipboard.writeText(formatted).then(() => { 789 const original = this.textContent; 790 this.textContent = "Copied!"; 791 setTimeout(() => { 792 this.textContent = original; 793 }, 1200); 794 }).catch(err => { 795 console.error("Clipboard error:", err); 796 }); 797 798 }); 799 }); 800}); 801</script>
vendor: 1 bytes, line 801
801
802<script id="quarto-html-after-body" type="application/javascript"> 803 window.document.addEventListener("DOMContentLoaded", function (event) { 804 // Ensure there is a toggle, if there isn't float one in the top right 805 if (window.document.querySelector('.quarto-color-scheme-toggle') === null) { 806 const a = window.document.createElement('a'); 807 a.classList.add('top-right'); 808 a.classList.add('quarto-color-scheme-toggle'); 809 a.href = ""; 810 a.onclick = function() { try { window.quartoToggleColorScheme(); } catch {} return false; }; 811 const i = window.document.createElement("i"); 812 i.classList.add('bi'); 813 a.appendChild(i); 814 window.document.body.appendChild(a); 815 } 816 setColorSchemeToggle(hasAlternateSentinel()) 817 const icon = "î§"; 818 const anchorJS = new window.AnchorJS(); 819 anchorJS.options = { 820 placement: 'right', 821 icon: icon 822 }; 823 anchorJS.add('.anchored'); 824 const isCodeAnnotation = (el) => { 825 for (const clz of el.classList) { 826 if (clz.startsWith('code-annotation-')) { 827 return true; 828 } 829 } 830 return false; 831 } 832 const onCopySuccess = function(e) { 833 // button target 834 const button = e.trigger; 835 // don't keep focus 836 button.blur(); 837 // flash "checked" 838 button.classList.add('code-copy-button-checked'); 839 var currentTitle = button.getAttribute("title"); 840 button.setAttribute("title", "Copied!"); 841 let tooltip; 842 if (window.bootstrap) { 843 button.setAttribute("data-bs-toggle", "tooltip"); 844 button.setAttribute("data-bs-placement", "left"); 845 button.setAttribute("data-bs-title", "Copied!"); 846 tooltip = new bootstrap.Tooltip(button, 847 { trigger: "manual", 848 customClass: "code-copy-button-tooltip", 849 offset: [0, -8]}); 850 tooltip.show(); 851 } 852 setTimeout(function() { 853 if (tooltip) { 854 tooltip.hide(); 855 button.removeAttribute("data-bs-title"); 856 button.removeAttribute("data-bs-toggle"); 857 button.removeAttribute("data-bs-placement"); 858 } 859 button.setAttribute("title", currentTitle); 860 button.classList.remove('code-copy-button-checked'); 861 }, 1000); 862 // clear code selection 863 e.clearSelection(); 864 } 865 const getTextToCopy = function(trigger) { 866 const outerScaffold = trigger.parentElement.cloneNode(true); 867 const codeEl = outerScaffold.querySelector('code'); 868 for (const childEl of codeEl.children) { 869 if (isCodeAnnotation(childEl)) { 870 childEl.remove(); 871 } 872 } 873 return codeEl.innerText; 874 } 875 const clipboard = new window.ClipboardJS('.code-copy-button:not([data-in-quarto-modal])', { 876 text: getTextToCopy 877 }); 878 clipboard.on('success', onCopySuccess); 879 if (window.document.getElementById('quarto-embedded-source-code-modal')) { 880 const clipboardModal = new window.ClipboardJS('.code-copy-button[data-in-quarto-modal]', { 881 text: getTextToCopy, 882 container: window.document.getElementById('quarto-embedded-source-code-modal') 883 }); 884 clipboardModal.on('success', onCopySuccess); 885 } 886 var localhostRegex = new RegExp(/^(?:http|https):\/\/localhost\:?[0-9]*\//); 887 var mailtoRegex = new RegExp(/^mailto:/); 888 var filterRegex = new RegExp('/' + window.location.host + '/'); 889 var isInternal = (href) => { 890 return filterRegex.test(href) || localhostRegex.test(href) || mailtoRegex.test(href); 891 } 892 // Inspect non-navigation links and adorn them if external 893 var links = window.document.querySelectorAll('a[href]:not(.nav-link):not(.navbar-brand):not(.toc-action):not(.sidebar-link):not(.sidebar-item-toggle):not(.pagination-link):not(.no-external):not([aria-hidden]):not(.dropdown-item):not(.quarto-navigation-tool):not(.about-link)'); 894 for (var i=0; i<links.length; i++) { 895 const link = links[i]; 896 if (!isInternal(link.href)) { 897 // undo the damage that might have been done by quarto-nav.js in the case of 898 // links that we want to consider external 899 if (link.dataset.originalHref !== undefined) { 900 link.href = link.dataset.originalHref; 901 } 902 } 903 } 904 function tippyHover(el, contentFn, onTriggerFn, onUntriggerFn) { 905 const config = { 906 allowHTML: true, 907 maxWidth: 500, 908 delay: 100,
909 arrow: false, 910 appendTo: function(el) { 911 return el.parentElement; 912 }, 913 interactive: true, 914 interactiveBorder: 10, 915 theme: 'quarto', 916 placement: 'bottom-start', 917 }; 918 if (contentFn) { 919 config.content = contentFn; 920 } 921 if (onTriggerFn) { 922 config.onTrigger = onTriggerFn; 923 } 924 if (onUntriggerFn) { 925 config.onUntrigger = onUntriggerFn; 926 } 927 window.tippy(el, config); 928 } 929 const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]'); 930 for (var i=0; i<noterefs.length; i++) { 931 const ref = noterefs[i]; 932 tippyHover(ref, function() { 933 // use id or data attribute instead here 934 let href = ref.getAttribute('data-footnote-href') || ref.getAttribute('href'); 935 try { href = new URL(href).hash; } catch {} 936 const id = href.replace(/^#\/?/, ""); 937 const note = window.document.getElementById(id); 938 if (note) { 939 return note.innerHTML; 940 } else { 941 return ""; 942 } 943 }); 944 } 945 const xrefs = window.document.querySelectorAll('a.quarto-xref'); 946 const processXRef = (id, note) => { 947 // Strip column container classes 948 const stripColumnClz = (el) => { 949 el.classList.remove("page-full", "page-columns"); 950 if (el.children) { 951 for (const child of el.children) { 952 stripColumnClz(child); 953 } 954 } 955 } 956 stripColumnClz(note) 957 if (id === null || id.startsWith('sec-')) { 958 // Special case sections, only their first couple elements 959 const container = document.createElement("div"); 960 if (note.children && note.children.length > 2) { 961 container.appendChild(note.children[0].cloneNode(true)); 962 for (let i = 1; i < note.children.length; i++) { 963 const child = note.children[i]; 964 if (child.tagName === "P" && child.innerText === "") { 965 continue; 966 } else { 967 container.appendChild(child.cloneNode(true)); 968 break; 969 } 970 } 971 if (window.Quarto?.typesetMath) { 972 window.Quarto.typesetMath(container); 973 } 974 return container.innerHTML 975 } else { 976 if (window.Quarto?.typesetMath) { 977 window.Quarto.typesetMath(note); 978 } 979 return note.innerHTML; 980 } 981 } else { 982 // Remove any anchor links if they are present 983 const anchorLink = note.querySelector('a.anchorjs-link'); 984 if (anchorLink) { 985 anchorLink.remove(); 986 } 987 if (window.Quarto?.typesetMath) { 988 window.Quarto.typesetMath(note); 989 } 990 if (note.classList.contains("callout")) { 991 return note.outerHTML; 992 } else { 993 return note.innerHTML; 994 } 995 } 996 } 997 for (var i=0; i<xrefs.length; i++) { 998 const xref = xrefs[i]; 999 tippyHover(xref, undefined, function(instance) { 1000 instance.disable(); 1001 let url = xref.getAttribute('href'); 1002 let hash = undefined; 1003 if (url.startsWith('#')) { 1004 hash = url; 1005 } else { 1006 try { hash = new URL(url).hash; } catch {} 1007 } 1008 if (hash) { 1009 const id = hash.replace(/^#\/?/, ""); 1010 const note = window.document.getElementById(id); 1011 if (note !== null) { 1012 try { 1013 const html = processXRef(id, note.cloneNode(true)); 1014 instance.setContent(html); 1015 } finally { 1016 instance.enable(); 1017 instance.show(); 1018 } 1019 } else { 1020 // See if we can fetch this 1021 fetch(url.split('#')[0]) 1022 .then(res => res.text()) 1023 .then(html => { 1024 const parser = new DOMParser(); 1025 const htmlDoc = parser.parseFromString(html, "text/html"); 1026 const note = htmlDoc.getElementById(id); 1027 if (note !== null) { 1028 const html = processXRef(id, note); 1029 instance.setContent(html); 1030 } 1031 }).finally(() => { 1032 instance.enable(); 1033 instance.show(); 1034 }); 1035 } 1036 } else { 1037 // See if we can fetch a full url (with no hash to target)
1038 // This is a special case and we should probably do some content thinning / targeting 1039 fetch(url) 1040 .then(res => res.text()) 1041 .then(html => { 1042 const parser = new DOMParser(); 1043 const htmlDoc = parser.parseFromString(html, "text/html"); 1044 const note = htmlDoc.querySelector('main.content'); 1045 if (note !== null) { 1046 // This should only happen for chapter cross references 1047 // (since there is no id in the URL) 1048 // remove the first header 1049 if (note.children.length > 0 && note.children[0].tagName === "HEADER") { 1050 note.children[0].remove(); 1051 } 1052 const html = processXRef(null, note); 1053 instance.setContent(html); 1054 } 1055 }).finally(() => { 1056 instance.enable(); 1057 instance.show(); 1058 }); 1059 } 1060 }, function(instance) { 1061 }); 1062 } 1063 let selectedAnnoteEl; 1064 const selectorForAnnotation = ( cell, annotation) => { 1065 let cellAttr = 'data-code-cell="' + cell + '"'; 1066 let lineAttr = 'data-code-annotation="' + annotation + '"'; 1067 const selector = 'span[' + cellAttr + '][' + lineAttr + ']'; 1068 return selector; 1069 } 1070 const selectCodeLines = (annoteEl) => { 1071 const doc = window.document; 1072 const targetCell = annoteEl.getAttribute("data-target-cell"); 1073 const targetAnnotation = annoteEl.getAttribute("data-target-annotation"); 1074 const annoteSpan = window.document.querySelector(selectorForAnnotation(targetCell, targetAnnotation)); 1075 const lines = annoteSpan.getAttribute("data-code-lines").split(","); 1076 const lineIds = lines.map((line) => { 1077 return targetCell + "-" + line; 1078 }) 1079 let top = null; 1080 let height = null; 1081 let parent = null; 1082 if (lineIds.length > 0) { 1083 //compute the position of the single el (top and bottom and make a div) 1084 const el = window.document.getElementById(lineIds[0]); 1085 top = el.offsetTop; 1086 height = el.offsetHeight; 1087 parent = el.parentElement.parentElement; 1088 if (lineIds.length > 1) { 1089 const lastEl = window.document.getElementById(lineIds[lineIds.length - 1]); 1090 const bottom = lastEl.offsetTop + lastEl.offsetHeight; 1091 height = bottom - top; 1092 } 1093 if (top !== null && height !== null && parent !== null) { 1094 // cook up a div (if necessary) and position it 1095 let div = window.document.getElementById("code-annotation-line-highlight"); 1096 if (div === null) { 1097 div = window.document.createElement("div"); 1098 div.setAttribute("id", "code-annotation-line-highlight"); 1099 div.style.position = 'absolute'; 1100 parent.appendChild(div); 1101 } 1102 div.style.top = top - 2 + "px"; 1103 div.style.height = height + 4 + "px"; 1104 div.style.left = 0; 1105 let gutterDiv = window.document.getElementById("code-annotation-line-highlight-gutter"); 1106 if (gutterDiv === null) { 1107 gutterDiv = window.document.createElement("div"); 1108 gutterDiv.setAttribute("id", "code-annotation-line-highlight-gutter"); 1109 gutterDiv.style.position = 'absolute'; 1110 const codeCell = window.document.getElementById(targetCell); 1111 const gutter = codeCell.querySelector('.code-annotation-gutter'); 1112 gutter.appendChild(gutterDiv); 1113 } 1114 gutterDiv.style.top = top - 2 + "px"; 1115 gutterDiv.style.height = height + 4 + "px"; 1116 } 1117 selectedAnnoteEl = annoteEl; 1118 } 1119 }; 1120 const unselectCodeLines = () => { 1121 const elementsIds = ["code-annotation-line-highlight", "code-annotation-line-highlight-gutter"]; 1122 elementsIds.forEach((elId) => { 1123 const div = window.document.getElementById(elId); 1124 if (div) { 1125 div.remove(); 1126 } 1127 }); 1128 selectedAnnoteEl = undefined; 1129 }; 1130 // Handle positioning of the toggle 1131 window.addEventListener( 1132 "resize", 1133 throttle(() => { 1134 elRect = undefined; 1135 if (selectedAnnoteEl) { 1136 selectCodeLines(selectedAnnoteEl); 1137 } 1138 }, 10) 1139 ); 1140 function throttle(fn, ms) { 1141 let throttle = false;
1142 let timer; 1143 return (...args) => { 1144 if(!throttle) { // first call gets through 1145 fn.apply(this, args); 1146 throttle = true; 1147 } else { // all the others get throttled 1148 if(timer) clearTimeout(timer); // cancel #2 1149 timer = setTimeout(() => { 1150 fn.apply(this, args); 1151 timer = throttle = false; 1152 }, ms); 1153 } 1154 }; 1155 } 1156 // Attach click handler to the DT 1157 const annoteDls = window.document.querySelectorAll('dt[data-target-cell]'); 1158 for (const annoteDlNode of annoteDls) { 1159 annoteDlNode.addEventListener('click', (event) => { 1160 const clickedEl = event.target; 1161 if (clickedEl !== selectedAnnoteEl) { 1162 unselectCodeLines(); 1163 const activeEl = window.document.querySelector('dt[data-target-cell].code-annotation-active'); 1164 if (activeEl) { 1165 activeEl.classList.remove('code-annotation-active'); 1166 } 1167 selectCodeLines(clickedEl); 1168 clickedEl.classList.add('code-annotation-active'); 1169 } else { 1170 // Unselect the line 1171 unselectCodeLines(); 1172 clickedEl.classList.remove('code-annotation-active'); 1173 } 1174 }); 1175 } 1176 const findCites = (el) => { 1177 const parentEl = el.parentElement; 1178 if (parentEl) { 1179 const cites = parentEl.dataset.cites; 1180 if (cites) { 1181 return { 1182 el, 1183 cites: cites.split(' ') 1184 }; 1185 } else { 1186 return findCites(el.parentElement) 1187 } 1188 } else { 1189 return undefined; 1190 } 1191 }; 1192 var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]'); 1193 for (var i=0; i<bibliorefs.length; i++) { 1194 const ref = bibliorefs[i]; 1195 const citeInfo = findCites(ref); 1196 if (citeInfo) { 1197 tippyHover(citeInfo.el, function() { 1198 var popup = window.document.createElement('div'); 1199 citeInfo.cites.forEach(function(cite) { 1200 var citeDiv = window.document.createElement('div'); 1201 citeDiv.classList.add('hanging-indent'); 1202 citeDiv.classList.add('csl-entry'); 1203 var biblioDiv = window.document.getElementById('ref-' + cite); 1204 if (biblioDiv) { 1205 citeDiv.innerHTML = biblioDiv.innerHTML; 1206 } 1207 popup.appendChild(citeDiv); 1208 }); 1209 return popup.innerHTML; 1210 }); 1211 } 1212 } 1213 }); 1214 </script>
1214 1215</div> <!-- /content --> 1216<footer class="footer"> 1217 <div class="nav-footer"> 1218 <div class="nav-footer-left"> 1219<p>Copyright 2026, Paul Bürkner</p> 1220</div> 1221 <div class="nav-footer-center"> 1222 1223 </div> 1224 <div class="nav-footer-right"> 1225 <ul class="footer-items list-unstyled"> 1226 <li class="nav-item"> 1227 <a class="nav-link" href="../impressum/index.html"> 1228<p>Impressum</p> 1229</a> 1230 </li> 1231</ul> 1232 </div> 1233 </div> 1234</footer> 1235 1236 1237 1238 1239</body></html>
Line numbers count LF bytes from the start of the resource, as the search results do. Vendor segments are library code the classifier recognised; they are stored but not indexed. Bytes are shown as Latin1 characters, one per byte.