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Asymptotic expansion of the posterior density in high dimensional generalized linear models

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  • Dasgupta, Shibasish
  • Khare, Kshitij
  • Ghosh, Malay

Abstract

While developing a prior distribution for any Bayesian analysis, it is important to check whether the corresponding posterior distribution becomes degenerate in the limit to the true parameter value as the sample size increases. In the same vein, it is also important to understand a more detailed asymptotic behavior of posterior distributions. This is particularly relevant in the development of many nonsubjective priors. The present paper focuses on asymptotic expansions of posteriors for generalized linear models with canonical link functions when the number of regressors grows to infinity at a certain rate relative to the growth of the sample size. These expansions are then used to derive moment matching priors in the generalized linear model setting.

Suggested Citation

  • Dasgupta, Shibasish & Khare, Kshitij & Ghosh, Malay, 2014. "Asymptotic expansion of the posterior density in high dimensional generalized linear models," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 126-148.
    • Handle: RePEc:eee:jmvana:v:131:y:2014:i:c:p:126-148
    DOI: 10.1016/j.jmva.2014.06.013
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    References listed on IDEAS

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    1. Ghosal, Subhashis, 2000. "Asymptotic Normality of Posterior Distributions for Exponential Families when the Number of Parameters Tends to Infinity," Journal of Multivariate Analysis, Elsevier, vol. 74(1), pages 49-68, July.
    2. Martin Crowder, 1988. "Asymptotic expansions of posterior expectations, distributions and densities for stochastic processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(2), pages 297-309, June.
    3. Subhashis Ghosal & Tapas Samanta, 1997. "Asymptotic Expansions of Posterior Distributions in Nonregular Cases," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 181-197, March.
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