## Electronic Journal of Statistics

### On Bayesian credible sets, restricted parameter spaces and frequentist coverage

#### 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.

#### Article information

Source
Electron. J. Statist., Volume 7 (2013), 1419-1431.

Dates
First available in Project Euclid: 21 May 2013

https://projecteuclid.org/euclid.ejs/1369148598

Digital Object Identifier
doi:10.1214/13-EJS806

Mathematical Reviews number (MathSciNet)
MR3066373

Zentralblatt MATH identifier
1336.62097

#### Citation

Marchand, Éric; Strawderman, William E. On Bayesian credible sets, restricted parameter spaces and frequentist coverage. Electron. J. Statist. 7 (2013), 1419--1431. doi:10.1214/13-EJS806. https://projecteuclid.org/euclid.ejs/1369148598

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