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Causal discovery algorithms infer causal relations from data based on several assumptions, including notably the absence of measurement error. However, this assumption is most likely violated in practical applications, which may result in…

Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…

Credible intervals and credible sets, such as highest posterior density (HPD) intervals, form an integral statistical tool in Bayesian phylogenetics, both for phylogenetic analyses and for development. Readily available for continuous…

Causal inference, especially in observational studies, relies on untestable assumptions about the true data-generating process. Sensitivity analysis helps us determine how robust our conclusions are when we alter these underlying…

This paper describes a Bayesian method for learning causal networks using samples that were selected in a non-random manner from a population of interest. Examples of data obtained by non-random sampling include convenience samples and…

The estimation of heterogeneous treatment effects in the potential outcome setting is biased when there exists model misspecification or unobserved confounding. As these biases are unobservable, what model to use when remains a critical…

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e.…

Boundary condition (BC) calibration to assimilate clinical measurements is an essential step in any subject-specific simulation of cardiovascular fluid dynamics. Bayesian calibration approaches have successfully quantified the uncertainties…

Anomaly detection methods identify examples that do not follow the expected behaviour, typically in an unsupervised fashion, by assigning real-valued anomaly scores to the examples based on various heuristics. These scores need to be…

We propose and evaluate two methods that validate the computation of Bayes factors: one based on an improved variant of simulation-based calibration checking (SBC) and one based on calibration metrics for binary predictions. We show that in…

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…

We evaluate the robustness of a probabilistic formulation of system identification (ID) to sparse, noisy, and indirect data. Specifically, we compare estimators of future system behavior derived from the Bayesian posterior of a learning…

Estimated uncertainty by approximate posteriors in Bayesian neural networks are prone to miscalibration, which leads to overconfident predictions in critical tasks that have a clear asymmetric cost or significant losses. Here, we extend the…

Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been…

For linear models with a diverging number of parameters, it has recently been shown that modified versions of Bayesian information criterion (BIC) can identify the true model consistently. However, in many cases there is little…

Pursuing invariant prediction from heterogeneous environments opens the door to learning causality in a purely data-driven way and has several applications in causal discovery and robust transfer learning. However, existing methods such as…

Constraint-based causal discovery is brittle in finite-sample regimes because erroneous conditional-independence (CI) decisions can cascade into substantial structural errors. We propose Quantitative Argumentation for Causal Discovery…

Diffusion models have impressive image generation capability, but low-quality generations still exist, and their identification remains challenging due to the lack of a proper sample-wise metric. To address this, we propose BayesDiff, a…

We develop and apply two calibration procedures for checking the coverage of approximate Bayesian credible sets including intervals estimated using Monte Carlo methods. The user has an ideal prior and likelihood, but generates a credible…

Learning causal relationships between pairs of complex traits from observational studies is of great interest across various scientific domains. However, most existing methods assume the absence of unmeasured confounding and restrict causal…