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The prior distribution for the unknown model parameters plays a crucial role in the process of statistical inference based on Bayesian methods. However, specifying suitable priors is often difficult even when detailed prior knowledge is…

When two nested models are compared, using a Bayes factor, from an objective standpoint, two seemingly conflicting issues emerge at the time of choosing parameter priors under the two models. On the one hand, for moderate sample sizes, the…

We extend the work of Hahn and Carvalho (2015) and develop a doubly-regularized sparse regression estimator by synthesizing Bayesian regularization with penalized least squares within a decision-theoretic framework. In contrast to existing…

While the choice of prior is one of the most critical parts of the Bayesian inference workflow, recent Bayesian deep learning models have often fallen back on vague priors, such as standard Gaussians. In this review, we highlight the…

As predictive models -- e.g., from machine learning -- give likely outcomes, they may be used to reason on the effect of an intervention, a causal-inference task. The increasing complexity of health data has opened the door to a plethora of…

The goal of causal inference is to understand the outcome of alternative courses of action. However, all causal inference requires assumptions. Such assumptions can be more influential than in typical tasks for probabilistic modeling, and…

The paper considers model selection in regression under the additional structural constraints on admissible models where the number of potential predictors might be even larger than the available sample size. We develop a Bayesian formalism…

Study of the bivariate normal distribution raises the full range of issues involving objective Bayesian inference, including the different types of objective priors (e.g., Jeffreys, invariant, reference, matching), the different modes of…

Logistic regression models for binomial responses are routinely used in statistical practice. However, the maximum likelihood estimate may not exist due to data separability. We address this issue by considering a conjugate prior penalty…

Choosing a shrinkage method can be done by selecting a penalty from a list of pre-specified penalties or by constructing a penalty based on the data. If a list of penalties for a class of linear models is given, we provide comparisons based…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

Machine learning algorithms may have disparate impacts on protected groups. To address this, we develop methods for Bayes-optimal fair classification, aiming to minimize classification error subject to given group fairness constraints. We…

For in vivo research experiments with small sample sizes and available historical data, we propose a sequential Bayesian method for the Behrens-Fisher problem. We consider it as a model choice question with two models in competition: one…

We introduce the concept of conjugate prior models for a given likelihood function in Bayesian spatial inversion. The conjugate class of prior models can be selection extended and still remain conjugate. We demonstrate the generality of…

The current standard Bayesian approach to model calibration, which assigns a Gaussian process prior to the discrepancy term, often suffers from issues of unidentifiability and computational complexity and instability. When the goal is to…

We introduce the BREASE framework for the Bayesian analysis of randomized controlled trials with a binary treatment and a binary outcome. Approaching the problem from a causal inference perspective, we propose parameterizing the likelihood…

Competing risks occur in survival analysis when multiple causes of death are present. They play a prominent role in several domains extending beyond biostatistics to encompass epidemiology, actuarial sciences, and reliability theory. This…

Competing risks models for a repairable system subject to several failure modes are discussed. Under minimal repair, it is assumed that each failure mode has a power law intensity. An orthogonal reparametrization is used to obtain an…

In model-based clustering, the Galaxy data set is often used as a benchmark data set to study the performance of different modeling approaches. Aitkin (2001) compares maximum likelihood and Bayesian analyses of the Galaxy data set and…

We develop a Bayesian framework for tackling the supervised clustering problem, the generic problem encountered in tasks such as reference matching, coreference resolution, identity uncertainty and record linkage. Our clustering model is…