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Asymptotic Expansion of the Posterior Based on Pairwise Likelihood

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  • Yang Wu

    (American Express Company)

  • Malay Ghosh

    (University of Florida)

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).

Suggested Citation

  • Yang Wu & Malay Ghosh, 2017. "Asymptotic Expansion of the Posterior Based on Pairwise Likelihood," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 39-75, February.
    • Handle: RePEc:spr:sankha:v:79:y:2017:i:1:d:10.1007_s13171-016-0094-y
    DOI: 10.1007/s13171-016-0094-y
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    References listed on IDEAS

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    1. S. le Cessie & J. C. van Houwelingen, 1994. "Logistic Regression for Correlated Binary Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 95-108, March.
    2. Cristiano Varin, 2008. "On composite marginal likelihoods," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(1), pages 1-28, February.
    3. D. R. Cox, 2004. "A note on pseudolikelihood constructed from marginal densities," Biometrika, Biometrika Trust, vol. 91(3), pages 729-737, September.
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