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This paper investigates the {\em nonasymptotic} properties of Bayes procedures for estimating an unknown distribution from $n$ i.i.d.\ observations. We assume that the prior is supported by a model $(\scr{S},h)$ (where $h$ denotes the…

Uncovering genuine relationships between a response variable of interest and a large collection of covariates is a fundamental and practically important problem. In the context of Gaussian linear models, both the Bayesian and non-Bayesian…

Bayesian inference is a widely used statistical method. The free energy and generalization loss, which are used to estimate the accuracy of Bayesian inference, are known to be small in singular models that do not have a unique optimal…

Simulation-based Bayesian inference (SBI) methods are widely used for parameter estimation in complex models where evaluating the likelihood is challenging but generating simulations is relatively straightforward. However, these methods…

Bayesian regression determines model parameters by minimizing the expected loss, an upper bound to the true generalization error. However, the loss ignores misspecification, where models are imperfect. Parameter uncertainties from Bayesian…

Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…

There has been significant progress in Bayesian inference based on sparsity-inducing (e.g., spike-and-slab and horseshoe-type) priors for high-dimensional regression models. The resulting posteriors, however, in general do not possess…

We study Bayesian approaches to causal inference via propensity score regression. Much of the Bayesian literature on propensity score methods have relied on approaches that cannot be viewed as fully Bayesian in the context of conventional…

Measurement error occurs when a covariate influencing a response variable is corrupted by noise. This can lead to misleading inference outcomes, particularly in problems where accurately estimating the relationship between covariates and…

We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a symmetrized Dirichlet process mixture of Gaussians. For the…

In this paper we construct optimal designs for frequentist model averaging estimation. We derive the asymptotic distribution of the model averaging estimate with fixed weights in the case where the competing models are non-nested and none…

This paper presents a Bayesian framework for assessing the adequacy of a model without the necessity of explicitly enumerating a specific alternate model. A test statistic is developed for tracking the performance of the model across…

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

We empirically show that Bayesian inference can be inconsistent under misspecification in simple linear regression problems, both in a model averaging/selection and in a Bayesian ridge regression setting. We use the standard linear model,…

Modern imaging techniques heavily rely on Bayesian statistical models to address difficult image reconstruction and restoration tasks. This paper addresses the objective evaluation of such models in settings where ground truth is…

Regularized system identification is the major advance in system identification in the last decade. Although many promising results have been achieved, it is far from complete and there are still many key problems to be solved. One of them…

This article considers Bayesian model selection via mean-field (MF) variational approximation. Towards this goal, we study the non-asymptotic properties of MF inference under the Bayesian framework that allows latent variables and model…

In Bayesian nonparametric inference, random discrete probability measures are commonly used as priors within hierarchical mixture models for density estimation and for inference on the clustering of the data. Recently, it has been shown…

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…

Simulation-based inference (SBI) methods such as approximate Bayesian computation (ABC), synthetic likelihood, and neural posterior estimation (NPE) rely on simulating statistics to infer parameters of intractable likelihood models.…