For estimating a lower bounded location or mean parameter for a symmetric and logconcave density, we investigate the frequentist performance of the 100(1 − α)% 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 − 3α/2 and 1 − 3α/2 + α2/1+α with thelower bound 1 − 3α/2 improving (for α ≤1/3) on the previously established (; ) lower bound 1−α/1+α. Several illustrative examples are given.
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Bayesian credible sets
- Confidence intervals
- Frequentist coverage probability
- Restricted parameter space