Properly constrained reference priors decay rates for efficient and robust posterior inference

TL;DR

This paper introduces two strategies for constraining reference priors in Bayesian analysis to ensure tractability and proper posteriors, emphasizing Jeffreys prior decay rates and demonstrating practical applicability.

Contribution

It proposes novel methods to incorporate constraints into reference priors, balancing objectivity with tractability and properness in Bayesian inference.

Findings

Two constraint strategies effectively produce tractable and proper reference priors.

The methods leverage Jeffreys prior decay rates for improved prior construction.

Practical example demonstrates applicability to real-world problems.

Abstract

In Bayesian analysis, reference priors are widely recognized for their objective nature. Yet, they often lead to intractable and improper priors, which complicates their application. Besides, informed prior elicitation methods are penalized by the subjectivity of the choices they require. In this paper, we aim at proposing a reconciliation of the aforementioned aspects. Leveraging the objective aspect of reference prior theory, we introduce two strategies of constraint incorporation to build tractable reference priors. One provides a simple and easy-to-compute solution when the improper aspect is not questioned, and the other introduces constraints to ensure the reference prior is proper, or it provides proper posterior. Our methodology emphasizes the central role of Jeffreys prior decay rates in this process, and the practical applicability of our results is demonstrated using an example taken from the literature.