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When do nonparametric Bayesian procedures ``overfit''? To shed light on this question, we consider a binary regression problem in detail and establish frequentist consistency for a certain class of Bayes procedures based on hierarchical…

Motivated by recently emerging problems in machine learning and statistics, we propose data models which relax the familiar i.i.d. assumption. In essence, we seek to understand what it means for data to come from a set of probability…

Throughout the life sciences we routinely seek to interpret measurements and observations using parameterised mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a…

Counterfactual explanations utilize feature perturbations to analyze the outcome of an original decision and recommend an actionable recourse. We argue that it is beneficial to provide several alternative explanations rather than a single…

End-to-end simulations play a key role in the analysis of any high-sensitivity CMB experiment, providing high-fidelity systematic error propagation capabilities unmatched by any other means. In this paper, we address an important issue…

When random effects are correlated with sample design variables, the usual approach of employing individual survey weights (constructed to be inversely proportional to the unit survey inclusion probabilities) to form a pseudo-likelihood no…

Model selection strategies have been routinely employed to determine a model for data analysis in statistics, and further study and inference then often proceed as though the selected model were the true model that were known a priori. This…

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.…

Note: Published now as a chapter in "Handbook of the History and Philosophy of Mathematical Practice" (Springer Nature, editor B. Sriraman, https://doi.org/10.1007/978-3-030-19071-2_105-1). The application of mathematical probability theory…

Posterior distributions on parameters computed from experimental data using Bayesian techniques are only as accurate as the models used to construct them. In many applications these models are incomplete, which both reduces the prospects of…

In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…

When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for…

The problem of testing mutually exclusive hypotheses with dependent test statistics is considered. Bayesian and frequentist approaches to multiplicity control are studied and compared to help gain understanding as to the effect of test…

The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…

Large-sample Bayesian analogs exist for many frequentist methods, but are less well-known for the widely-used 'sandwich' or 'robust' variance estimates. We review existing approaches to Bayesian analogs of sandwich variance estimates and…

Quantifying model uncertainty is critical for understanding prediction reliability, yet distinguishing between aleatoric and epistemic uncertainty remains challenging. We extend recent work from classification to regression to provide a…

For a Bayesian, real-time forecasting with the posterior predictive distribution can be challenging for a variety of time series models. First, estimating the parameters of a time series model can be difficult with sample-based approaches…

In many hypothesis testing applications, we have mixed priors, with well-motivated informative priors for some parameters but not for others. The Bayesian methodology uses the Bayes factor and is helpful for the informative priors, as it…

We propose a general method to carry out a valid Bayesian analysis of a finite-dimensional `targeted' parameter in the presence of a finite-dimensional nuisance parameter. We apply our methods to causal inference based on estimating…

In computational inverse problems, it is common that a detailed and accurate forward model is approximated by a computationally less challenging substitute. The model reduction may be necessary to meet constraints in computing time when…