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On the Lebesgue decomposition of the posterior distribution with respect to the prior in regular Bayesian experiments

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  • Macci, Claudio

Abstract

Given a regular Bayesian experiment we can consider the Lebesgue decomposition of the posterior distributions w.r.t. the prior. Then, by using the Lebesgue decomposition of each sampling distribution w.r.t. the predictive distribution, we show that the absolutely continuous parts of the posteriors are only determined by the absolutely continuous parts of the sampling distributions, while the singular parts of the posteriors are only determined by the singular parts.

Suggested Citation

  • Macci, Claudio, 1996. "On the Lebesgue decomposition of the posterior distribution with respect to the prior in regular Bayesian experiments," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 147-152, February.
    • Handle: RePEc:eee:stapro:v:26:y:1996:i:2:p:147-152
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    Cited by:

    1. Macci, Claudio & Polettini, Silvia, 2001. "Bayes factor for non-dominated statistical models," Statistics & Probability Letters, Elsevier, vol. 53(1), pages 79-89, May.
    2. Macci, Claudio, 1998. "The maximal dominated subsets of a statistical experiment," Statistics & Probability Letters, Elsevier, vol. 39(3), pages 185-193, August.

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