Asymptotic Expansion of the Posterior Based on Pairwise Likelihood

Yang Wu () and Malay Ghosh ()
Additional contact information
Yang Wu: American Express Company
Malay Ghosh: University of Florida

Sankhya A: The Indian Journal of Statistics, 2017, vol. 79, issue 1, No 3, 39-75

Abstract: Abstract This paper provides an asymptotic expansion of the posterior based on pairwise likelihood instead of the regular likelihood. The celebrated Bernstein-von Mises theorem is derived as a special case. A multiparameter version of the asymptotic expansion is also given involving nuisance parameters. As a direct application of these expansions, one can obtain moment matching priors and quantile matching priors with or without nuisance parameters. A simulation study is provided verifying this agreement between frequentist quantiles and Bayesian quantiles using quantile matching priors. One of the major tools used in this paper is strong consistency of the maximum pairwise likelihood estimator (MPLE).

Keywords: Asymptotic theory; Pseudo likelihood; Strong consistency; Taylor expansion; Moment matching priors; Quantile matching priors; Primary:; 62F15; Secondary:; F12 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s13171-016-0094-y

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