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On sufficient conditions for Bayesian consistency

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  • Stephen Walker

Abstract

This paper contributes to the theory of Bayesian consistency for a sequence of posterior and predictive distributions arising from an independent and identically distributed sample. A new sufficient condition for posterior Hellinger consistency is presented which provides motivation for recent results appearing in the literature. Such motivation is important since current sufficient conditions are not known to be necessary. It also provides new insights into Bayesian consistency. A new consistency theorem for the sequence of predictive densities is given. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • Stephen Walker, 2003. "On sufficient conditions for Bayesian consistency," Biometrika, Biometrika Trust, vol. 90(2), pages 482-488, June.
    • Handle: RePEc:oup:biomet:v:90:y:2003:i:2:p:482-488
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    Cited by:

    1. Tang, Yongqiang & Ghosal, Subhashis, 2007. "A consistent nonparametric Bayesian procedure for estimating autoregressive conditional densities," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4424-4437, May.
    2. Stephen Walker & Eduardo Gutiérrez-Peña, 2011. "A decision-theoretical view of default priors," Theory and Decision, Springer, vol. 70(1), pages 1-11, January.
    3. Pierpaolo De Blasi & Lancelot F. James & John W. Lau, 2007. "Bayesian Nonparametric Estimation and Consistency of Mixed Multinomial Logit Choice Models," ICER Working Papers - Applied Mathematics Series 15-2007, ICER - International Centre for Economic Research.

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