Asymptotic Expansion of the Posterior Based on Pairwise Likelihood

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).