The Department of Statistics and Actuarial Science Fall Colloquium Series presents:

Jonathan Bradley, Associate Professor, and Associate Director, Center for Spatio-Temporal Statistics in AI, Department of Statistics and Data Science, University of Missouri

"Scalable AI-Calibrated Bayesian Hierarchical Models"

Abstract: We develop a Bayesian hierarchical model where one can sample independent replicates directly from the joint posterior distribution for all unknowns in generalized linear mixed model contexts. The model can handle data distributed according to the exponential family, and allows for several different dependent data covariance assumptions (e.g., spatial, multivariate, space-time, etc.). One can sample independent replicates directly from the marginal posterior distribution of fixed and random effects primarily due to the use of a discrepancy term. Informative samples of the hyperparameters from the posterior distribution are achieved via a constrained Bayesian approach, where posterior samples favor "small values" of an out-of-sample criterion (e.g., cross-validation). Specifically, this criterion is specified to have smaller out-of-sample error as compared to a chosen AI method. The resulting posterior distribution has a form that one can sample from directly without Markov chain Monte Carlo (MCMC) and without approximate Bayesian strategies (i.e., this approach is exact). Our use of out-sample-criteria leads to a fully Bayesian strategy for finite samples that produces a particular M-open property for continuous hyperparameters, where under certain conditions, produces posterior summaries that outperform the chosen AI method in terms of the out-of-sample criterion. We compare with fully Bayesian inference using the unconstrained discrepancy model, and apply our proposed method to analyze an environmental dataset.

Meet and Greet at 3:15 pm in 241 SH. Colloquium at 3:30 pm in 61 SH.