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Sensitivity analyses reveal the influence of various modeling choices on the outcomes of statistical analyses. While theoretically appealing, they are overwhelmingly inefficient for complex Bayesian models. In this work, we propose…

Amortized Bayesian inference (ABI) with neural networks has emerged as a powerful simulation-based approach for estimating complex mechanistic models. However, extending ABI to hierarchical models, a cornerstone of modern Bayesian analysis,…

Quantitative Methods · Quantitative Biology 2026-04-08 Jonas Arruda , Vikas Pandey , Catherine Sherry , Margarida Barroso , Xavier Intes , Jan Hasenauer , Stefan T. Radev

As models of cognition grow in complexity and number of parameters, Bayesian inference with standard methods can become intractable, especially when the data-generating model is of unknown analytic form. Recent advances in simulation-based…

Machine Learning · Statistics 2020-07-14 Stefan T. Radev , Andreas Voss , Eva Marie Wieschen , Paul-Christian Bürkner

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…

Machine Learning · Statistics 2026-03-04 Aayush Mishra , Daniel Habermann , Marvin Schmitt , Stefan T. Radev , Paul-Christian Bürkner

Bayesian inference usually requires running potentially costly inference procedures separately for every new observation. In contrast, the idea of amortized Bayesian inference is to initially invest computational cost in training an…

Machine Learning · Computer Science 2023-05-25 Manuel Glöckler , Michael Deistler , Jakob H. Macke

Complex simulator-based models are now routinely used to perform inference across the sciences and engineering, but existing inference methods are often unable to account for outliers and other extreme values in data which occur due to…

Machine Learning · Statistics 2026-02-18 Ayush Bharti , Charita Dellaporta , Yuga Hikida , François-Xavier Briol

Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex and large-scale predictive problems. The recent success of deep neural…

Machine Learning · Statistics 2026-01-14 Roy Shivam Ram Shreshtth , Arnab Hazra , Gourab Mukherjee

Finite mixtures are a broad class of models useful in scenarios where observed data is generated by multiple distinct processes but without explicit information about the responsible process for each data point. Estimating Bayesian mixture…

Machine Learning · Statistics 2026-03-17 Šimon Kucharský , Paul Christian Bürkner

Amortized Bayesian inference (ABI) offers fast, scalable approximations to posterior densities by training neural surrogates on data simulated from the statistical model. However, ABI methods are highly sensitive to model misspecification:…

Machine Learning · Statistics 2026-01-27 Šimon Kucharský , Aayush Mishra , Daniel Habermann , Stefan T. Radev , Paul-Christian Bürkner

Unbinned likelihood fits aim at maximizing the information one can extract from experimental data, yet their application in realistic statistical analyses is often hindered by the computational cost of profiling systematic uncertainties.…

High Energy Physics - Phenomenology · Physics 2026-02-16 Davide Valsecchi , Mauro Donegà , Rainer Wallny

Despite their outstanding performance in a broad spectrum of real-world tasks, deep artificial neural networks are sensitive to input noises, particularly adversarial perturbations. On the contrary, human and animal brains are much less…

Neural and Evolutionary Computing · Computer Science 2022-05-23 Xiyuan Chen , Xingyu Li , Yi Zhou , Tianming Yang

Recent advances in probabilistic deep learning enable efficient amortized Bayesian inference in settings where the likelihood function is only implicitly defined by a simulation program (simulation-based inference; SBI). But how faithful is…

Machine Learning · Computer Science 2024-06-07 Marvin Schmitt , Paul-Christian Bürkner , Ullrich Köthe , Stefan T. Radev

High-level theories rooted in the Bayesian Brain Hypothesis often frame cognitive effort as the cost of resolving the conflict between habits and optimal policies. In parallel, evidence accumulator models (EAMs) provide a mechanistic…

Neurons and Cognition · Quantitative Biology 2025-09-15 Alvaro Garrido Perez , Viktor Lemoine , Amrapali Pednekar , Yara Khaluf , Pieter Simoens

Individual-based models of contagious processes are useful for predicting epidemic trajectories and informing intervention strategies. In such models, the incorporation of contact network information can capture the non-randomness and…

Populations and Evolution · Quantitative Biology 2023-11-09 Maxwell H. Wang , Jukka-Pekka Onnela

Graphs arise across diverse domains, from biology and chemistry to social and information networks, as well as in transportation and logistics. Inference on graph-structured data requires methods that are permutation-invariant, scalable…

Machine Learning · Statistics 2026-05-05 Svenja Jedhoff , Elizaveta Semenova , Aura Raulo , Anne Meyer , Paul-Christian Bürkner

Amortized Bayesian inference trains neural networks to solve stochastic inference problems using model simulations, thereby making it possible to rapidly perform Bayesian inference for any newly observed data. However, current…

Machine Learning · Computer Science 2024-07-16 Manuel Gloeckler , Michael Deistler , Christian Weilbach , Frank Wood , Jakob H. Macke

Bayesian simulation-based inference (SBI) methods are used in statistical models where simulation is feasible but the likelihood is intractable. Standard SBI methods can perform poorly in cases of model misspecification, and there has been…

Methodology · Statistics 2025-04-15 Wang Yuyan , Michael Evans , David J. Nott

Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…

Machine Learning · Statistics 2025-12-22 Yuli Slavutsky , David M. Blei

We study how the training data distribution affects confidence and performance in image classification models. We introduce Embedding Density, a model-agnostic framework that estimates prediction confidence by measuring the distance of test…

Machine Learning · Computer Science 2026-01-28 Maksim Kazanskii , Artem Kasianov

Our work utilized a non-sequential simulation-based inference algorithm to provide an amortized neural density estimator, which approximates the posterior distribution for seven parameters of the adaptive exponential integrate-and-fire…

Neural and Evolutionary Computing · Computer Science 2026-02-13 Jakob Kaiser , Eric Müller , Johannes Schemmel
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