A Modification for Bayesian Credible Intervals

• Published in: Communications in statistics. Theory and methods Vol. 35; no. 9; pp. 1703 - 1711
• Main Author: Zhang, Tonglin
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01-09-2006; Taylor & Francis
• Subjects: Bayesian credible intervals; Decision theory; Exact sciences and technology; Frequentist coverage probability; Location parameters; Mathematics; Posterior coverage probability; Prior and posterior distributions; Probability and statistics; Sciences and techniques of general use; Statistics; Unimodality; Bayes estimation; Unimodality; Density estimation; Prior distribution; Bayesian credible intervals; Location parameter; Mean estimation; Posterior coverage probability; Prior and posterior distributions; Unimodality. 62C10; Statistical method; Coverage probability; Frequentist coverage probability; Posterior probability; Location parameters; Posterior distribution
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610920600683838

In Bayesian analysis, people usually report the highest posterior density (HPD) credible interval as an interval estimate of an unknown parameter. However, when the unknown parameter is the nonnegative normal mean, the Bayesian HPD credible interval under the uniform prior has quite a low minimum frequentist coverage probability. To enhance the minimum frequentist coverage probability of a credible interval, I propose a new method of reporting the Bayesian credible interval. Numerical results show that the new reported credible interval has a much higher minimum frequentist coverage probability than the HPD credible interval.