Weak Informativity and the Information in One Prior Relative to Another

TL;DR

This paper proposes a method to quantify and compare the informativeness of different priors relative to a base prior, using measures of prior-data conflict, to aid in selecting conservative priors.

Contribution

It introduces a novel approach to characterize the informativeness of priors relative to a base prior through prior-data conflict measures.

Findings

Provides a framework for comparing priors based on information content.

Offers criteria for selecting conservative priors in Bayesian analysis.

Enhances understanding of prior influence in statistical modeling.

Abstract

A question of some interest is how to characterize the amount of information that a prior puts into a statistical analysis. Rather than a general characterization, we provide an approach to characterizing the amount of information a prior puts into an analysis, when compared to another base prior. The base prior is considered to be the prior that best reflects the current available information. Our purpose then is to characterize priors that can be used as conservative inputs to an analysis relative to the base prior. The characterization that we provide is in terms of a priori measures of prior-data conflict.