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267<span class="menu-text">Research</span></a>
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341<h1 class="title">Research Projects</h1>
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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 – 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 “learning” 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 – 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 – 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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{jedhoff2026efficient,&amp;#10; author = {Jedhoff, S. and Kutabi, H. and Meyer, A. and Bürkner, P. C.},&amp;#10;    title = {Efficient Uncertainty Propagation in Bayesian Two-Step Procedures},&amp;#10;   journal = {ArXiv preprint},&amp;#10;    year = {2026}&amp;#10;}" role="button">BibTeX</span></p></li>
398<li><p>Kühmichel, L., Huang, J. M., Pratz, V., Arruda, J., Olischläger, H., Habermann, D., Kucharský, Š., 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,&amp;#10;  author = {Kühmichel, L. and Huang, J. M. and Pratz, V. and Arruda, J. and Olischläger, H. and Habermann, D. and Kucharský, Š. and Elsemüller, L. and Mishra, A. and Bracher, N. and Jedhoff, S. and Schmitt, M. and Bürkner, P. C. and Radev, S. T.},&amp;#10;  title = {BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python},&amp;#10; journal = {ArXiv preprint},&amp;#10;    year = {2026}&amp;#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,&amp;#10; author = {Riha, A. E. and Jedhoff, S. and Bürkner, P. C. and Vehtari, A.},&amp;#10; title = {Approximating Bayesian Leave-One-Group-out Cross-Validation},&amp;#10; journal = {ArXiv preprint},&amp;#10;    year = {}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{jedhoff2026mice,&amp;#10;
400  author = {Jedhoff, S. and Semenova, E. and Raulo, A. and Meyer, A. and Bürkner, P. C.},&amp;#10;    title = {From Mice to Trains: Amortized Bayesian Inference on Graph Data},&amp;#10; journal = {Transactions in Machine Learning Research},&amp;#10; year = {2026}&amp;#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 – 2027</p>
417<p>Publications:</p>
418<ul>
419<li><p>Kucharský, Š., <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,&amp;#10;   author = {Kucharský, Š. and Mishra, A. and Habermann, D. and Radev, S. T. and Bürkner, P. C.},&amp;#10; title = {Improving the Accuracy of Amortized Model Comparison with Self-Consistency},&amp;#10;  journal = {ArXiv preprint},&amp;#10;    year = {2026}&amp;#10;}" role="button">BibTeX</span></p></li>
420<li><p>Kühmichel, L., Huang, J. M., Pratz, V., Arruda, J., Olischläger, H., Habermann, D., Kucharský, Š., 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,&amp;#10;  author = {Kühmichel, L. and Huang, J. M. and Pratz, V. and Arruda, J. and Olischläger, H. and Habermann, D. and Kucharský, Š. and Elsemüller, L. and Mishra, A. and Bracher, N. and Jedhoff, S. and Schmitt, M. and Bürkner, P. C. and Radev, S. T.},&amp;#10;  title = {BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python},&amp;#10; journal = {ArXiv preprint},&amp;#10;    year = {2026}&amp;#10;}" role="button">BibTeX</span></p></li>
421<li><p><strong>Mishra, A.</strong>, Kucharský, Š., 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,&amp;#10; author = {Mishra, A. and Kucharský, Š. and Bürkner, P. C.},&amp;#10;    title = {Unsupervised Continual Learning for Amortized Bayesian Inference},&amp;#10;    journal = {ArXiv preprint},&amp;#10;    year = {2026}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mishra2026robust,&amp;#10; author = {Mishra, A. and Habermann, D. and Schmitt, M. and Radev, S. T. and Bürkner, P. C.},&amp;#10;   title = {Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data},&amp;#10;  journal = {International Conference on Learning Representations (ICLR)},&amp;#10;   year = {2026}&amp;#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 – 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, Š., 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,&amp;#10;  author = {Kühmichel, L. and Huang, J. M. and Pratz, V. and Arruda, J. and Olischläger, H. and Habermann, D. and Kucharský, Š. and Elsemüller, L. and Mishra, A. and Bracher, N. and Jedhoff, S. and Schmitt, M. and Bürkner, P. C. and Radev, S. T.},&amp;#10;  title = {BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python},&amp;#10; journal = {ArXiv preprint},&amp;#10;    year = {2026}&amp;#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,&amp;#10;   author = {Müller, J. and Kühmichel, L. and Rohbeck, M. and Radev, S. T. and Köthe, U.},&amp;#10;    title = {Towards Context-Aware Domain Generalization: Understanding the Benefits and Limits of Marginal Transfer Learning},&amp;#10;    journal = {ArXiv preprint},&amp;#10;    year = {2025}&amp;#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,&amp;#10; author = {Bracher, N. and Kühmichel, L. and Ivanova, D. R. and Intes, X. and Bürkner, P. C. and Radev, S. T.},&amp;#10; title = {JADAI: Jointly Amortizing Adaptive Design and Bayesian Inference},&amp;#10;    journal = {Proceedings of the International Conference on Machine Learning (ICML)},&amp;#10;    year = {2025}&amp;#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,&amp;#10;   author = {Habermann, D. and Schmitt, M. and Kühmichel, L. and Bulling, A. and Radev, S. T. and Bürkner, P. C.},&amp;#10;    title = {Amortized Bayesian Multilevel Models},&amp;#10;    journal = {Bayesian Analysis},&amp;#10; year = {2025},&amp;#10; doi = {10.1214/25-BA1570}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{Pogorelyuk2025stable,&amp;#10; author = {Pogorelyuk, L. and Bracher, N. L. and Verkleeren, A. and Kühmichel, L. and Radev, S. T.},&amp;#10;    title = {Stable Single-Pixel Contrastive Learning for Semantic and Geometric Tasks},&amp;#10;   journal = {NeurIPS Workshop on Unifying Representations in Neural Models},&amp;#10; year = {2025}&amp;#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 method’s 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">Šimon 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 – 2027</p>
462<p>Publications:</p>
463<ul>
464<li><p><strong>Kucharský, Š.</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,&amp;#10;   author = {Kucharský, Š. and Mishra, A. and Habermann, D. and Radev, S. T. and Bürkner, P. C.},&amp;#10; title = {Improving the Accuracy of Amortized Model Comparison with Self-Consistency},&amp;#10;  journal = {ArXiv preprint},&amp;#10;    year = {2026}&amp;#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, Š.</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,&amp;#10;  author = {Kühmichel, L. and Huang, J. M. and Pratz, V. and Arruda, J. and Olischläger, H. and Habermann, D. and Kucharský, Š. and Elsemüller, L. and Mishra, A. and Bracher, N. and Jedhoff, S. and Schmitt, M. and Bürkner, P. C. and Radev, S. T.},&amp;#10;  title = {BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python},&amp;#10; journal = {ArXiv preprint},&amp;#10;    year = {2026}&amp;#10;}" role="button">BibTeX</span></p></li>
466<li><p>Mishra, A., <strong>Kucharský, Š.</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,&amp;#10; author = {Mishra, A. and Kucharský, Š. and Bürkner, P. C.},&amp;#10;    title = {Unsupervised Continual Learning for Amortized Bayesian Inference},&amp;#10;    journal = {ArXiv preprint},&amp;#10;    year = {2026}&amp;#10;}" role="button">BibTeX</span></p></li>
467<li><p><strong>Kucharský, Š.</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,&amp;#10; author = {Kucharský, Š. and Bürkner, P. C.},&amp;#10;   title = {Amortized Bayesian Mixture Models},&amp;#10;   journal = {Statistics and Computing},&amp;#10;  year = {2026},&amp;#10; doi = {10.1007/s11222-026-10911-y}&amp;#10;}" role="button">BibTeX</span></p></li>
468<li><p><strong>Kucharský, Š.</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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{kucharsky2025amortized,&amp;#10;   author = {Kucharský, Š. and Bürkner, P. C.},&amp;#10;   title = {Amortized Bayesian Cognitive Modeling with BayesFlow},&amp;#10;    journal = {PsyArXiv preprint},&amp;#10; year = {2025},&amp;#10; doi = {10.31234/osf.io/34k6q_v1}&amp;#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 – 2026</p>
498<p>Publications:</p>
499<ul>
500<li><p>Kucharský, Š., 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,&amp;#10;   author = {Kucharský, Š. and Mishra, A. and Habermann, D. and Radev, S. T. and Bürkner, P. C.},&amp;#10; title = {Improving the Accuracy of Amortized Model Comparison with Self-Consistency},&amp;#10;  journal = {ArXiv preprint},&amp;#10;    year = {2026}&amp;#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, Š., 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,&amp;#10;  author = {Kühmichel, L. and Huang, J. M. and Pratz, V. and Arruda, J. and Olischläger, H. and Habermann, D. and Kucharský, Š. and Elsemüller, L. and Mishra, A. and Bracher, N. and Jedhoff, S. and Schmitt, M. and Bürkner, P. C. and Radev, S. T.},&amp;#10;  title = {BayesFlow 2.0: Multi-Backend Amortized Bayesian Inference in Python},&amp;#10; journal = {ArXiv preprint},&amp;#10;    year = {2026}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mishra2026robust,&amp;#10; author = {Mishra, A. and Habermann, D. and Schmitt, M. and Radev, S. T. and Bürkner, P. C.},&amp;#10;   title = {Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data},&amp;#10;  journal = {International Conference on Learning Representations (ICLR)},&amp;#10;   year = {2026}&amp;#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,&amp;#10;   author = {Habermann, D. and Schmitt, M. and Kühmichel, L. and Bulling, A. and Radev, S. T. and Bürkner, P. C.},&amp;#10;    title = {Amortized Bayesian Multilevel Models},&amp;#10;    journal = {Bayesian Analysis},&amp;#10; year = {2025},&amp;#10; doi = {10.1214/25-BA1570}&amp;#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,&amp;#10;    author = {Schmitt, M. and Ivanova, D. R. and Habermann, D. and Köthe, U. and Bürkner, P. C. and Radev, S. T.},&amp;#10; title = {Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference},&amp;#10; journal = {Proceedings of the International Conference on Machine Learning (ICML)},&amp;#10;    year = {2024}&amp;#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 – 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,&amp;#10;  author = {Bockting, F. and Bürkner, P. C.},&amp;#10;    title = {elicito: A Python Package for Expert Prior Elicitation},&amp;#10;  journal = {ArXiv preprint},&amp;#10;    year = {2025}&amp;#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,&amp;#10;   author = {Bockting, F. and Radev, S. T. and Bürkner, P. C.},&amp;#10;   title = {Expert-elicitation method for non-parametric joint priors using normalizing flows},&amp;#10;   journal = {Statistics and Computing},&amp;#10;  year = {2025},&amp;#10; doi = {0.1007/s11222-025-10665-z}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{bockting2024simulation,&amp;#10;   author = {Bockting, F. and Radev, S. T. and Bürkner, P. C.},&amp;#10;   title = {Simulation-Based Prior Knowledge Elicitation for Parametric Bayesian Models},&amp;#10; journal = {Scientific Reports},&amp;#10;    year = {2024},&amp;#10; doi = {10.1038/s41598-024-68090-7}&amp;#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 processes’ 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 – 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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{fazio2026latent,&amp;#10;  author = {Fazio, L. and Bürkner, P. C.},&amp;#10;   title = {Latent Variable Models for Distributional Features},&amp;#10;  journal = {ArXiv preprint},&amp;#10;    year = {2026}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{fazio2025primed,&amp;#10;  author = {Fazio, L. and Scholz, M. and Aguilar, J. E. and Bürkner, P. C.},&amp;#10; title = {Primed Priors for Simulation-Based Validation of Bayesian Models},&amp;#10;    journal = {ArXiv preprint},&amp;#10;    year = {2025}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{fazio2025gaussian,&amp;#10;    author = {Fazio, L. and Bürkner, P. C.},&amp;#10;   title = {Gaussian distributional structural equation models: A framework for modeling latent heteroscedasticity},&amp;#10;  journal = {Multivariate Behavioral Research},&amp;#10;  year = {2025},&amp;#10; doi = {10.1080/00273171.2025.2483252}&amp;#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 – 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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mukherjee2025latent,&amp;#10;  author = {Mukherjee, S. and Aguilar, J. E. and Zago, M. and Claassen, M. and Bürkner, P. C.},&amp;#10;  title = {Latent variable estimation with composite Hilbert space Gaussian processes},&amp;#10;  journal = {ArXiv preprint},&amp;#10;    year = {2025}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mukherjee2025hilbert,&amp;#10; author = {Mukherjee, S. and Claassen, M. and Bürkner, P. C.},&amp;#10;  title = {Hilbert space methods for approximating multi-output latent variable Gaussian processes},&amp;#10; journal = {Statistics and Computing},&amp;#10;  year = {2026},&amp;#10; doi = {10.1007/s11222-026-10869-x}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mukherjee2025dgplvm,&amp;#10;  author = {Mukherjee, S. and Claassen, M. and Bürkner, P. C.},&amp;#10;  title = {DGP-LVM: Derivative Gaussian process latent variable models},&amp;#10; journal = {Statistics and Computing},&amp;#10;  year = {2025},&amp;#10; doi = {10.1007/s11222-025-10644-4}&amp;#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 – 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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{reiser2026bayesian,&amp;#10;   author = {Reiser, P. and Bürkner, P. C. and Guthke, A.},&amp;#10;   title = {Bayesian Surrogate Training on Multiple Data Sources: A Hybrid Modeling Strategy},&amp;#10;    journal = {Statistics and Computing},&amp;#10;  year = {2026},&amp;#10; doi = {10.1007/s11222-026-10906-9}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{scheurer2026uncertainty,&amp;#10;  author = {Scheurer, S. and Reiser, P. and Brünnette, T. and Nowak, W. and Guthke, A. and Bürkner, P. C.},&amp;#10;  title = {Uncertainty-Aware Surrogate-based Amortized Bayesian Inference for Computationally Expensive Models},&amp;#10; journal = {Transactions in Machine Learning Research},&amp;#10; year = {2026}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{reiser2025uncertainty,&amp;#10;    author = {Reiser, P. and Aguilar, J. E. and Guthke, A. and Bürkner, P. C.},&amp;#10;    title = {Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference},&amp;#10;    journal = {Statistics and Computing},&amp;#10;  year = {2025},&amp;#10; doi = {10.1007/s11222-025-10597-8}&amp;#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 models’ 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 – 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 – 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,&amp;#10;  author = {Li, C. and Vehtari, A. and Bürkner, P. C. and Radev, S. T. and Acerbi, L. and Schmitt, M.},&amp;#10;  title = {Amortized Bayesian Workflow},&amp;#10; journal = {Transactions in Machine Learning Research},&amp;#10; year = {2026}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mishra2026robust,&amp;#10; author = {Mishra, A. and Habermann, D. and Schmitt, M. and Radev, S. T. and Bürkner, P. C.},&amp;#10;   title = {Robust Amortized Bayesian Inference with Self-Consistency Losses on Unlabeled Data},&amp;#10;  journal = {International Conference on Learning Representations (ICLR)},&amp;#10;   year = {2026}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{sailynoja2026posterior,&amp;#10;   author = {Säilynoja, T. and Schmitt, M. and Bürkner, P. C. and Vehtari, A.},&amp;#10;   title = {Posterior SBC: Simulation-Based Calibration Checking Conditional on Data},&amp;#10;    journal = {Statistics and Computing},&amp;#10;  year = {2026},&amp;#10; doi = {10.1007/s11222-026-10825-9}&amp;#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,&amp;#10;   author = {Habermann, D. and Schmitt, M. and Kühmichel, L. and Bulling, A. and Radev, S. T. and Bürkner, P. C.},&amp;#10;    title = {Amortized Bayesian Multilevel Models},&amp;#10;    journal = {Bayesian Analysis},&amp;#10; year = {2025},&amp;#10; doi = {10.1214/25-BA1570}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{elsemueller2024sensitivity,&amp;#10;   author = {Elsemüller, L. and Olischläger, H. and Schmitt, M. and Bürkner, P. C. and Köthe, U. and Radev, S. T.},&amp;#10;   title = {Sensitivity-Aware Amortized Bayesian Inference},&amp;#10;  journal = {Transactions in Machine Learning Research},&amp;#10; year = {2024}&amp;#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,&amp;#10;   author = {Schmitt, M. and Hikida, Y. and Radev, S. T. and Sadlo, F. and Bürkner, P. C.},&amp;#10;   title = {The Simplex Projection: Lossless Visualization of 4D Compositional Data on a 2D Canvas},&amp;#10;  journal = {ArXiv preprint},&amp;#10;    year = {2024},&amp;#10; doi = {10.48550/arXiv.2403.11141}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{schmitt2025detecting,&amp;#10; author = {Schmitt, M. and Bürkner, P. C. and Köthe, U. and Radev, S. T.},&amp;#10;  title = {Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks: An Extended Investigation},&amp;#10;    journal = {ArXiv preprint},&amp;#10;    year = {2024},&amp;#10; doi = {10.48550/arXiv.2406.03154}&amp;#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,&amp;#10;   author = {Schmitt, M. and Pratz, V. and Köthe, U. and Bürkner, P. C. and Radev, S. T.},&amp;#10;    title = {Consistency Models for Scalable and Fast Simulation-Based Inference},&amp;#10; journal = {Proceedings of the Conference on Neural Information Processing Systems (NeurIPS)},&amp;#10;  year = {2024}&amp;#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,&amp;#10;    author = {Schmitt, M. and Ivanova, D. R. and Habermann, D. and Köthe, U. and Bürkner, P. C. and Radev, S. T.},&amp;#10; title = {Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference},&amp;#10; journal = {Proceedings of the International Conference on Machine Learning (ICML)},&amp;#10;    year = {2024}&amp;#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,&amp;#10;  author = {Schmitt, M. and Radev, S. T. and Bürkner, P. C.},&amp;#10;    title = {Fuse It or Lose It: Deep Fusion for Multimodal Simulation-Based Inference},&amp;#10;   journal = {ArXiv preprint},&amp;#10;    year = {2024},&amp;#10; doi = {10.48550/arXiv.2311.10671}&amp;#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 &amp; 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,&amp;#10;    author = {Radev, S. T. and Schmitt, M. and Pratz, V. and Picchini, U. and Köthe, U. and Bürkner, P. C.},&amp;#10;   title = {JANA: Jointly Amortized Neural Approximation of Complex Bayesian Models},&amp;#10; journal = {Uncertainty in Artificial Intelligence (UAI) Conference Proceedings},&amp;#10;   year = {2023}&amp;#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,&amp;#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.},&amp;#10;  title = {BayesFlow: Amortized Bayesian Workflows With Neural Networks},&amp;#10;    journal = {Journal of Open Source Software},&amp;#10;   year = {2023},&amp;#10; doi = {10.21105/joss.05702}&amp;#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 &amp; 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,&amp;#10;  author = {Schmitt, M. and Radev, S. T. and Bürkner, P. C.},&amp;#10;    title = {Meta-Uncertainty in Bayesian Model Comparison},&amp;#10;   journal = {Artificial Intelligence and Statistics (AISTATS) Conference Proceedings},&amp;#10;   year = {2023}&amp;#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 &amp; 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,&amp;#10; author = {Schmitt, M. and Bürkner, P. C. and Köthe, U. and Radev, S. T.},&amp;#10;  title = {Detecting Model Misspecification in Amortized Bayesian Inference with Neural Networks},&amp;#10;   journal = {Proceedings of the German Conference on Pattern Recognition (GCPR)},&amp;#10;    year = {2023},&amp;#10; doi = {10.1007/978-3-031-54605-1_35}&amp;#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 – 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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{aguilar2025dependency,&amp;#10;    author = {Aguilar, J. E. and Bürkner, P. C.},&amp;#10;  title = {Dependency-Aware Shrinkage Priors for High Dimensional Regression},&amp;#10;   journal = {ArXiv preprint},&amp;#10;    year = {2025}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{aguilar2025r2priors,&amp;#10;  author = {Aguilar, J. E. and Kohns, D. and Vehtari, A. and Bürkner, P. C.},&amp;#10;    title = {R2 priors for Grouped Variance Decomposition in High-dimensional Regression},&amp;#10; journal = {ArXiv preprint},&amp;#10;    year = {2025}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{fazio2025primed,&amp;#10;  author = {Fazio, L. and Scholz, M. and Aguilar, J. E. and Bürkner, P. C.},&amp;#10; title = {Primed Priors for Simulation-Based Validation of Bayesian Models},&amp;#10;    journal = {ArXiv preprint},&amp;#10;    year = {2025}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{mukherjee2025latent,&amp;#10;  author = {Mukherjee, S. and Aguilar, J. E. and Zago, M. and Claassen, M. and Bürkner, P. C.},&amp;#10;  title = {Latent variable estimation with composite Hilbert space Gaussian processes},&amp;#10;  journal = {ArXiv preprint},&amp;#10;    year = {2025}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{aguilar2025generalized,&amp;#10;   author = {Aguilar, J. E. and Bürkner, P. C.},&amp;#10;  title = {Generalized Decomposition Priors on R2},&amp;#10;  journal = {Bayesian Analysis},&amp;#10; year = {2025},&amp;#10; doi = {10.1214/25-BA1524}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{reiser2025uncertainty,&amp;#10;    author = {Reiser, P. and Aguilar, J. E. and Guthke, A. and Bürkner, P. C.},&amp;#10;    title = {Uncertainty Quantification and Propagation in Surrogate-based Bayesian Inference},&amp;#10;    journal = {Statistics and Computing},&amp;#10;  year = {2025},&amp;#10; doi = {10.1007/s11222-025-10597-8}&amp;#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 &amp; 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,&amp;#10; author = {Aguilar, J. E. and Bürkner, P. C.},&amp;#10;  title = {Intuitive Joint Priors for Bayesian Linear Multilevel Models: The R2D2M2 prior},&amp;#10;  journal = {Electronic Journal of Statistics},&amp;#10;  year = {2023},&amp;#10; doi = {10.1214/23-EJS2136}&amp;#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">
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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 user’s 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 – 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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{fazio2025primed,&amp;#10;  author = {Fazio, L. and Scholz, M. and Aguilar, J. E. and Bürkner, P. C.},&amp;#10; title = {Primed Priors for Simulation-Based Validation of Bayesian Models},&amp;#10;    journal = {ArXiv preprint},&amp;#10;    year = {2025}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{scholz2025prediction,&amp;#10; author = {Scholz, M. and Bürkner, P. C.},&amp;#10;  title = {Prediction can be safely used as a proxy for explanation in causally consistent Bayesian generalized linear models},&amp;#10;  journal = {Journal of Statistical Computation and Simulation},&amp;#10; year = {2025},&amp;#10; doi = {10.1080/00949655.2024.2449534}&amp;#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,&amp;#10; author = {Bürkner, P. C. and Scholz, M. and Radev, S. T.},&amp;#10; title = {Some models are useful, but how do we know which ones? Towards a unified Bayesian model taxonomy},&amp;#10;    journal = {Statistics Surveys},&amp;#10;    year = {2023},&amp;#10; doi = {10.1214/23-SS145}&amp;#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 &amp; Data</a> <span class="btn btn-outline-primary btn-xs" data-bibtex="@article{scholz2023posterior,&amp;#10;  author = {Scholz, M. and Bürkner, P. C.},&amp;#10;  title = {Posterior accuracy and calibration under misspecification in Bayesian generalized linear models},&amp;#10; journal = {ArXiv preprint},&amp;#10;    year = {2023},&amp;#10; doi = {10.48550/arXiv.2311.09081}&amp;#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
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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      &nbsp;
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>

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