Research

Hierarchical Bayesian modeling is the default approach in Bayesian analysis. However, existing Bayesian methods struggle to fit hierarchical models with many parameters on massive data sets. To address this issue, we develop a divide-and-conquer method based on score-based diffusion models. Our method scales to hundreds of thousands of parameters and enables fully Bayesian fluoresence lifetime imaging (FLI) under low signal-to-noise conditions.

Simulations play important and diverse roles in statistical workflows, for example, in model specification, checking, validation, and inference. Over the past decades, the application areas and overall potential of simulations in statistical workflows have expanded significantly, driven by the development of new AI-assisted methods and exponentially increasing computational resources. In this paper, we examine past and current trends in the field and offer perspectives on how simulations may shape the future of statistical practice.

Neural networks are fragile when confronted with data that significantly deviates from their training distribution. This is true in particular for models trained on simulated data and deployed for inference on real-world observations. We formalize the targets of trustworthy inference and systematically test unsupervised domain adaptation (UDA) methods that align embeddings of simulated and real data. We find that UDA reduces noise-related errors, but can cause unexpected failures when the model’s prior assumptions are wrong.

Cognitive models can estimate latent parameters from reaction time and accuracy data, capturing aspects like processing speed and decision caution. We examined how these parameters relate to real-world outcomes—education, income, and job prestige—in a large online sample. While overall effects were small, variability in processing speed (drift rate) was the strongest and most consistent predictor, highlighting the value of behavioral data science for generating new hypotheses about overlooked measures in cognitive modeling.

We present consistency models for posterior estimation (CMPE), a new free-form generative model family grounded in diffusion model theory. CMPE enables rapid few-shot inference with an unconstrained architecture that can be flexibly tailored to the model’s symmetry. We provide hyperparameters that support consistency training over a wide range of different dimensions, including low-dimensional ones which are important in simulaton-based inference but were previously difficult to tackle.

Cognitive processes naturally fluctuate over time, and superstatistics offer a flexible way to capture these non-stationary dynamics in cognitive models. We provide the first experimental validation of this approach by comparing four time-varying diffusion decision models in a perceptual task with controlled difficulty and speed-accuracy conditions. Using deep learning for efficient Bayesian estimation, we find that models allowing both gradual and abrupt parameter changes best match the data, suggesting that the inferred dynamics reflect genuine shifts in cognitive states.

Sensitivity analyses can reveal how different modeling choices affect statistical results, but they’re often too slow for complex Bayesian models. We introduce sensitivity-aware amortized Bayesian inference (SA-ABI) as an efficient method that (1) uses weight sharing to capture similarities between model versions with little extra cost, (2) exploits the speed of neural networks to test sensitivity to data and preprocessing changes, and (3) applies deep ensembles to spot sensitivity caused by poor fit. Our experiments show that SA-ABI can provide automatic insights into hidden uncertainties.

We improve amortized Bayesian inference by inverting Bayes’ theorem to estimate the implicit model evidence. We leverage the observation that deviations from constant evidence reveal approximation errors, which we penalize through a novel self-consistency loss. This loss improves inference quality in low-data regimes and boosts the training of neural density estimators across synthetic and real-world models.

Generative AI enables efficient simulation-based inference (SBI) for complex models. But how faithful is such inference if the simulation represents reality somewhat inaccurately? We conceptualize the types of simulation gaps arising in SBI and investigate how neural network outputs gradually deteriorate as a consequence. To notify users about this problem, we propose a new measure that can be trained in an unsupervised way. We show that our measure warns users about suspicious outputs, raises an alarm when predictions are not trustworthy, and guides model designers in their search for better simulators.

Bayesian model comparison (BMC) is a formal way to assess the relative merits of competing computational models. However, BMC is often intractable for hierarchical models due to their large number of parameters. To address this issue, we propose a deep learning method for performing BMC on any set of hierarchical models that can be instantiated as probabilistic programs. In addition to unlocking the ability to compare previously intractable models, our method enables re-estimation of model probabilities and fast performance validation prior to any real-data application.