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2013 On Bayesian credible sets, restricted parameter spaces and frequentist coverage
Éric Marchand, William E. Strawderman
Electron. J. Statist. 7: 1419-1431 (2013). DOI: 10.1214/13-EJS806

Abstract

For estimating a lower bounded parametric function in the framework of Marchand and Strawderman [6], we provide through a unified approach a class of Bayesian confidence intervals with credibility $1-\alpha$ and frequentist coverage probability bounded below by $\frac{1-\alpha}{1+\alpha}$. In cases where the underlying pivotal distribution is symmetric, the findings represent extensions with respect to the specification of the credible set achieved through the choice of a spending function, and include Marchand and Strawderman’s HPD procedure result. For non-symmetric cases, the determination of a such a class of Bayesian credible sets fills a gap in the literature and includes an “equal-tails” modification of the HPD procedure. Several examples are presented demonstrating wide applicability.

Citation

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Éric Marchand. William E. Strawderman. "On Bayesian credible sets, restricted parameter spaces and frequentist coverage." Electron. J. Statist. 7 1419 - 1431, 2013. https://doi.org/10.1214/13-EJS806

Information

Published: 2013
First available in Project Euclid: 21 May 2013

zbMATH: 1336.62097
MathSciNet: MR3066373
Digital Object Identifier: 10.1214/13-EJS806

Subjects:
Primary: 62C10, 62F15, 62F25, 62F30

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

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