On the frequentist coverage of Bayesian credible intervals for lower bounded means

TL;DR

This paper analyzes the frequentist coverage of Bayesian credible intervals for lower bounded means, revealing bounds and properties that improve understanding of their performance in symmetric, log-concave densities.

Contribution

It precisely characterizes the minimum coverage of Bayesian HPD credible sets for lower bounded means, providing new bounds and properties that improve upon previous results.

Findings

Minimum coverage is bounded between 1 - 3α/2 and 1 - 3α/2 + α^2/(1+α)

Lower bound 1 - 3α/2 improves previous bounds for α ≤ 1/3

Provides illustrative examples demonstrating theoretical results

Abstract

For estimating a lower bounded location or mean parameter for a symmetric and logconcave density, we investigate the frequentist performance of the $100(1-\alpha)%$ Bayesian HPD credible set associated with priors which are truncations of flat priors onto the restricted parameter space. Various new properties are obtained. Namely, we identify precisely where the minimum coverage is obtained and we show that this minimum coverage is bounded between $1-\frac{3\alpha}{2}$ and $1-\frac{3\alpha}{2}+\frac{\alpha^2}{1+\alpha}$; with the lower bound $1-\frac{3\alpha}{2}$ improving (for $\alpha \leq 1/3$) on the previously established ([9]; [8]) lower bound $\frac{1-\alpha}{1+\alpha}$. Several illustrative examples are given.