Checking for prior-data conflict using prior to posterior divergences

TL;DR

This paper introduces a Bayesian model checking method that detects prior-data conflicts by comparing observed divergence measures to their prior predictive distribution, enhancing model validation practices.

Contribution

A new approach for prior-data conflict detection using prior to posterior divergence, with extensions to hierarchical models and computational strategies like variational approximations.

Findings

Method effectively detects conflicts in complex models

Extensions to hierarchical Bayesian models demonstrated

Variational approximations reduce computational burden

Abstract

When using complex Bayesian models to combine information, the checking for consistency of the information being combined is good statistical practice. Here a new method is developed for detecting prior-data conflicts in Bayesian models based on comparing the observed value of a prior to posterior divergence to its distribution under the prior predictive distribution for the data. The divergence measure used in our model check is a measure of how much beliefs have changed from prior to posterior, and can be thought of as a measure of the overall size of a relative belief function. It is shown that the proposed method is intuitive, has desirable properties, can be extended to hierarchical settings, and is related asymptotically to Jeffreys' and reference prior distributions. In the case where calculations are difficult, the use of variational approximations as a way of relieving the computational burden is suggested. The methods are compared in a number of examples with an alternative but closely related approach in the literature based on the prior predictive distribution of a minimal sufficient statistic.