Bayesian Checking of the Second Levels of Hierarchical Models

TL;DR

This paper explores Bayesian methods for checking the adequacy of hierarchical models, emphasizing objective approaches suitable for preliminary data analysis, and compares various proposals through multiple examples.

Contribution

It introduces and critically evaluates Bayesian model checking techniques for hierarchical models without relying on informative priors, filling a gap in model validation methods.

Findings

Objective Bayesian methods are effective for model checking.

Different proposals for Bayesian model checking are compared.

The paper provides practical examples illustrating the methods.

Abstract

Hierarchical models are increasingly used in many applications. Along with this increased use comes a desire to investigate whether the model is compatible with the observed data. Bayesian methods are well suited to eliminate the many (nuisance) parameters in these complicated models; in this paper we investigate Bayesian methods for model checking. Since we contemplate model checking as a preliminary, exploratory analysis, we concentrate on objective Bayesian methods in which careful specification of an informative prior distribution is avoided. Numerous examples are given and different proposals are investigated and critically compared.