Criterion constrained Bayesian hierarchical models

Qingying Zong () and Jonathan R. Bradley ()
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Qingying Zong: Florida State University
Jonathan R. Bradley: Florida State University

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2023, vol. 32, issue 1, No 11, 294-320

Abstract: Abstract The goal of this article is to improve the predictive performance of a Bayesian hierarchical statistical model by incorporating a criterion typically used for model selection. In this article, 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 (i.e., the parameter space of the mean represents the candidate set of models). Specifically, we select a subset of our Bayesian hierarchical statistical model’s parameter space with high predictive performance (as measured by a criterion). Explicitly, 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. The CPE is a general 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 a lower squared error than Bayesian model averaging. Additional theoretical results are provided asthe 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 in a single model.

Keywords: Bayesian hierarchical model; Markov chain Monte Carlo; Posterior predictive p value; Information theory; Gaussian Processes; 62H11; 62F15 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11749-022-00834-x

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