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Asymptotic Normality of Posterior Distributions for Exponential Families when the Number of Parameters Tends to Infinity

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  • Ghosal, Subhashis

Abstract

We study consistency and asymptotic normality of posterior distributions of the natural parameter for an exponential family when the dimension of the parameter grows with the sample size. Under certain growth restrictions on the dimension, we show that the posterior distributions concentrate in neighbourhoods of the true parameter and can be approximated by an appropriate normal distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:74:y:2000:i:1:p:49-68
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    Cited by:

    1. Jing Zhou & Anirban Bhattacharya & Amy H. Herring & David B. Dunson, 2015. "Bayesian Factorizations of Big Sparse Tensors," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1562-1576, December.
    2. Jin, Xin & Bhattacharya, Anirban & Ghosh, Riddhi Pratim, 2024. "High-dimensional Bernstein–von Mises theorem for the Diaconis–Ylvisaker prior," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    3. 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.
    4. Alexandre Belloni & Victor Chernozhukov, 2014. "Posterior inference in curved exponential families under increasing dimensions," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 75-100, June.
    5. Banerjee, Sayantan & Ghosal, Subhashis, 2015. "Bayesian structure learning in graphical models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 147-162.
    6. Daniele Durante & David B. Dunson & Joshua T. Vogelstein, 2017. "Nonparametric Bayes Modeling of Populations of Networks," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1516-1530, October.

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