On Bayesian credible sets in restricted parameter space problems and lower bounds for frequentist coverage

2012/07/31 by Éric Marchand, Marchand, Eric, William E. Strawderman +1
Computer Science · Decision Sciences · Engineering · #62C10 #62F15 #62F25 #62F30 #FOS: Mathematics #Nuclear reactor physics and engineering #Probabilistic and Robust Engineering Design #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.1208.0028

openalex publication_date 2012/07/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

For estimating a lower bounded parametric function in the framework of Marchand and Strawderman (2006), we provide through a unified approach a class of Bayesian confidence intervals with credibility 1-α and frequentist coverage probability bounded below by (1-α)/(1+α). 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 \it 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.

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