Second-order matching prior family parametrized by sample size and matching probability

Toyoto Tanaka, Yoshihiro Hirose () and Fumiyasu Komaki
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Toyoto Tanaka: Tokio Marine & Nichido Fire Insurance Co., Ltd.
Yoshihiro Hirose: Hokkaido University
Fumiyasu Komaki: The University of Tokyo

Statistical Papers, 2020, vol. 61, issue 4, No 17, 1717 pages

Abstract: Abstract We propose a family of priors that satisfies the second-order probability matching property. The posterior quantile of a probability matching prior is exactly or approximately equal to the frequentist one. Most models lack an exact matching prior. If all quantiles of a prior’s posterior converge to the frequentist ones up to $$o(n^{-1/2})$$ o ( n - 1 / 2 ) or $$o(n^{-1})$$ o ( n - 1 ) as the sample size n increases, the prior is called a first-order probability matching prior and a second-order probability matching prior, respectively. Although a second-order matching prior does not necessarily exist, a first-order matching prior always exists. We introduce a class of priors that depend on the sample size and matching probability. We derive the condition under which the family satisfies the second-order probability matching property even when a second-order probability matching prior does not exist. The superiority of the proposed priors is illustrated in several numerical experiments.

Keywords: Bayesian asymptotics; Frequentist validity; Posterior quantile; Probability matching prior; 62F05; 62F15; 62F25 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s00362-018-1001-5

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