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Empirical Priors and Posterior Concentration Rates for a Monotone Density

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  • Ryan Martin

    (North Carolina State University)

Abstract

In a Bayesian context, prior specification for inference on monotone densities is conceptually straightforward, but proving posterior convergence theorems is complicated by the fact that desirable prior concentration properties often are not satisfied. In this paper, I first develop a new prior designed specifically to satisfy an empirical version of the prior concentration property, and then I give sufficient conditions on the prior inputs such that the corresponding empirical Bayes posterior concentrates around the true monotone density at nearly the optimal minimax rate. Numerical illustrations also reveal the practical benefits of the proposed empirical Bayes approach compared to Dirichlet process mixtures.

Suggested Citation

  • Ryan Martin, 2019. "Empirical Priors and Posterior Concentration Rates for a Monotone Density," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 493-509, December.
    • Handle: RePEc:spr:sankha:v:81:y:2019:i:2:d:10.1007_s13171-018-0147-5
    DOI: 10.1007/s13171-018-0147-5
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    References listed on IDEAS

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    1. Groeneboom,Piet & Jongbloed,Geurt, 2014. "Nonparametric Estimation under Shape Constraints," Cambridge Books, Cambridge University Press, number 9780521864015, October.
    2. Vytaras Brazauskas & Andreas Kleefeld, 2016. "Modeling Severity and Measuring Tail Risk of Norwegian Fire Claims," North American Actuarial Journal, Taylor & Francis Journals, vol. 20(1), pages 1-16, January.
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