This article reviews Bayesian inference from the perspective that the designated model is
misspecified. This misspecification has implications in interpretation of objects, such as the …

We consider the asymptotic behavior of posterior distributions and Bayes estimators for
infinite-dimensional statistical models. We give general results on the rate of convergence of …

This book has grown out of several courses that we have given over the years at Purdue
University, Michigan State University and the Indian Statistical Institute on Bayesian …

We review the current state of nonparametric Bayesian inference. The discussion follows a
list of important statistical inference problems, including density estimation, regression …

We study the rates of convergence of the maximum likelihood estimator (MLE) and posterior
distribution in density estimation problems, where the densities are location or location-scale …

This paper studies convergence behavior of latent mixing measures that arise in finite and
infinite mixture models, using transportation distances (ie, Wasserstein metrics). The …

We compute the rate at which the posterior distribution concentrates around the true
parameter value. The spaces we work in are quite general and include infinite dimensional …

Discrete random probability measures and the exchangeable random partitions they induce
are key tools for addressing a variety of estimation and prediction problems in Bayesian …

Statistics is intertwined with science and mathematics but is a subset of neither. The
“foundations of statistics” is the set of concepts that makes statistics a distinct field. For …

Abstract We propose Dirichlet Process mixtures of Generalized Linear Models (DP-GLM), a
new class of methods for nonparametric regression. Given a data set of input-response …