Frequency Coverage Properties of a Uniform Shrinkage Prior Distribution

TL;DR

This paper investigates the frequency properties of a uniform shrinkage prior in random-effects models, showing that its optimal shape parameter aligns with an improper flat prior for better Bayesian interval estimates.

Contribution

It identifies the optimal shape parameter for the USP that ensures better frequency coverage in Bayesian interval estimates of random effects.

Findings

USP achieves best frequency properties when it mimics an improper flat prior.

Empirical results show improved confidence level accuracy with optimal shape parameter.

The study applies to univariate and multivariate Gaussian hierarchical models.

Abstract

A uniform shrinkage prior (USP) distribution on the unknown variance component of a random-effects model is known to produce good frequency properties. The USP has a parameter that determines the shape of its density function, but it has been neglected whether the USP can maintain such good frequency properties regardless of the choice for the shape parameter. We investigate which choice for the shape parameter of the USP produces Bayesian interval estimates of random effects that meet their nominal confidence levels better than several existent choices in the literature. Using univariate and multivariate Gaussian hierarchical models, we empirically show that the USP can achieve its best frequency properties when its shape parameter makes the USP behave similarly to an improper flat prior distribution on the unknown variance component.