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On Bayesian consistency

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  • Stephen Walker
  • Nils Lid Hjort

Abstract

We consider a sequence of posterior distributions based on a data‐dependent prior (which we shall refer to as a pseudoposterior distribution) and establish simple conditions under which the sequence is Hellinger consistent. It is shown how investigations into these pseudo posteriors assist with the understanding of some true posterior distributions, including Pólya trees, the infinite dimensional exponential family and mixture models.

Suggested Citation

  • Stephen Walker & Nils Lid Hjort, 2001. "On Bayesian consistency," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 811-821.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:4:p:811-821
    DOI: 10.1111/1467-9868.00314
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    Citations

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    Cited by:

    1. Shively, Thomas S. & Walker, Stephen G. & Damien, Paul, 2011. "Nonparametric function estimation subject to monotonicity, convexity and other shape constraints," Journal of Econometrics, Elsevier, vol. 161(2), pages 166-181, April.
    2. Chen, Su & Walker, Stephen G., 2023. "A New Statistic for Bayesian Hypothesis Testing," Econometrics and Statistics, Elsevier, vol. 26(C), pages 139-152.
    3. Valen E. Johnson & David Rossell, 2010. "On the use of non‐local prior densities in Bayesian hypothesis tests," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 143-170, March.
    4. Jeremy Fouliard & Michael Howell & Hélène Rey & Vania Stavrakeva, 2020. "Answering the Queen: Machine Learning and Financial Crises," NBER Working Papers 28302, National Bureau of Economic Research, Inc.
    5. Luo, Yu & Graham, Daniel J. & McCoy, Emma J., 2023. "Semiparametric Bayesian doubly robust causal estimation," LSE Research Online Documents on Economics 117944, London School of Economics and Political Science, LSE Library.
    6. Thomas S. Shively & Thomas W. Sager & Stephen G. Walker, 2009. "A Bayesian approach to non‐parametric monotone function estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 159-175, January.
    7. C Rohrbeck & D A Costain & A Frigessi, 2018. "Bayesian spatial monotonic multiple regression," Biometrika, Biometrika Trust, vol. 105(3), pages 691-707.
    8. Ho, Chi-san & Damien, Paul & Walker, Stephen, 2017. "Bayesian mode regression using mixtures of triangular densities," Journal of Econometrics, Elsevier, vol. 197(2), pages 273-283.
    9. P. G. Bissiri & C. C. Holmes & S. G. Walker, 2016. "A general framework for updating belief distributions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 1103-1130, November.

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