Constrained Bayesian Hierarchical Models for Gaussian Data: A Criterion Based Approach

• Activity Number: 557 - New Directions in Bayesian Methods for Longitudinal and Graph Data
• Type: Contributed
• Date/Time: Thursday, August 11, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Qingying Zong* and Jonathan R Bradley
• Companies: Florida state university and Florida State University
• Keywords: Bayesian hierarchical model; Markov chain Monte Carlo; Information theory; Gaussian Processes

Abstract

The goal of this project is to improve the predictive performance of a Bayesian hierarchical statistical model by incorporating a criterion typically used for model selection. We view the problem of prediction of a latent real-valued mean as a model selection problem, where the candidate models are from an uncountable infinite set. Specifically, we select a subset of our Bayesian hierarchical statistical model’s parameter space with high predictive performance measured by a criterion. We truncate the joint support of the data and the parameter space of a given Bayesian hierarchical model to only include small values of the covariance penalized error (CPE) criterion, which is an expression that contains several information criteria as special cases. Simulation results show that as long as the truncated set does not have near-zero probability, we tend to obtain lower mean squared error than Bayesian model averaging. Additional theoretical results are provided that provide the foundation for these observations. We apply our approach to a dataset consisting of American Community Survey period estimates to illustrate that this perspective can lead to improvements of a single model.