Lasse Elsemüller

Lasse Elsemüller, Martin Schnuerch, Paul-Christian Bürkner et al.

Bayesian model comparison (BMC) offers a principled approach for assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular class of hierarchical models due to their high-dimensional nested parameter structure. To address this intractability, we propose a deep learning method for performing BMC on any set of hierarchical models which can be instantiated as probabilistic programs. Since our method enables amortized inference, it allows efficient re-estimation of posterior model probabilities and fast performance validation prior to any real-data application. In a series of extensive validation studies, we benchmark the performance of our method against the state-of-the-art bridge sampling method and demonstrate excellent amortized inference across all BMC settings. We then showcase our method by comparing four hierarchical evidence accumulation models that have previously been deemed intractable for BMC due to partly implicit likelihoods. Additionally, we demonstrate how transfer learning can be leveraged to enhance training efficiency. We provide reproducible code for all analyses and an open-source implementation of our method.

Lasse Elsemüller, Hans Olischläger, Marvin Schmitt et al.

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 sensitivity-aware amortized Bayesian inference (SA-ABI), a multifaceted approach to efficiently integrate sensitivity analyses into simulation-based inference with neural networks. First, we utilize weight sharing to encode the structural similarities between alternative likelihood and prior specifications in the training process with minimal computational overhead. Second, we leverage the rapid inference of neural networks to assess sensitivity to data perturbations and preprocessing steps. In contrast to most other Bayesian approaches, both steps circumvent the costly bottleneck of refitting the model for each choice of likelihood, prior, or data set. Finally, we propose to use deep ensembles to detect sensitivity arising from unreliable approximation (e.g., due to model misspecification). We demonstrate the effectiveness of our method in applied modeling problems, ranging from disease outbreak dynamics and global warming thresholds to human decision-making. Our results support sensitivity-aware inference as a default choice for amortized Bayesian workflows, automatically providing modelers with insights into otherwise hidden dimensions.

Stefan T Radev, Marvin Schmitt, Lukas Schumacher et al.

Modern Bayesian inference involves a mixture of computational techniques for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows for data analysis. Typical problems in Bayesian workflows are the approximation of intractable posterior distributions for diverse model types and the comparison of competing models of the same process in terms of their complexity and predictive performance. This manuscript introduces the Python library BayesFlow for simulation-based training of established neural network architectures for amortized data compression and inference. Amortized Bayesian inference, as implemented in BayesFlow, enables users to train custom neural networks on model simulations and re-use these networks for any subsequent application of the models. Since the trained networks can perform inference almost instantaneously, the upfront neural network training is quickly amortized.

Lars Kühmichel, Jerry M. Huang, Valentin Pratz et al.

Modern Bayesian inference involves a mixture of computational methods for estimating, validating, and drawing conclusions from probabilistic models as part of principled workflows. An overarching motif of many Bayesian methods is that they are relatively slow, which often becomes prohibitive when fitting complex models to large data sets. Amortized Bayesian inference (ABI) offers a path to solving the computational challenges of Bayes. ABI trains neural networks on model simulations, rewarding users with rapid inference of any model-implied quantity, such as point estimates, likelihoods, or full posterior distributions. In this work, we present the Python library BayesFlow, Version 2.0, for general-purpose ABI. Along with direct posterior, likelihood, and ratio estimation, the software includes support for multiple popular deep learning backends, a rich collection of generative networks for sampling and density estimation, complete customization and high-level interfaces, as well as new capabilities for hyperparameter optimization, design optimization, and hierarchical modeling. Using a case study on dynamical system parameter estimation, combined with comparisons to similar software, we show that our streamlined, user-friendly workflow has strong potential to support broad adoption.

Lasse Elsemüller, Valentin Pratz, Mischa von Krause et al.

Neural networks are fragile when confronted with data that significantly deviates from their training distribution. This is true in particular for simulation-based inference methods, such as neural amortized Bayesian inference (ABI), where models trained on simulated data are deployed on noisy real-world observations. Recent robust approaches employ unsupervised domain adaptation (UDA) to match the embedding spaces of simulated and observed data. However, the lack of comprehensive evaluations across different domain mismatches raises concerns about the reliability in high-stakes applications. We address this gap by systematically testing UDA approaches across a wide range of misspecification scenarios in silico and practice. We demonstrate that aligning summary spaces between domains effectively mitigates the impact of unmodeled phenomena or noise. However, the same alignment mechanism can lead to failures under prior misspecifications - a critical finding with practical consequences. Our results underscore the need for careful consideration of misspecification types when using UDA to increase the robustness of ABI.