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Converting information into probability measures with the Kullback–Leibler divergence

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  • Pier Bissiri
  • Stephen Walker

Abstract

This paper uses a decision theoretic approach for updating a probability measure representing beliefs about an unknown parameter. A cumulative loss function is considered, which is the sum of two terms: one depends on the prior belief and the other one on further information obtained about the parameter. Such information is thus converted to a probability measure and the key to this process is shown to be the Kullback–Leibler divergence. The Bayesian approach can be derived as a natural special case. Some illustrations are presented. Copyright The Institute of Statistical Mathematics, Tokyo 2012

Suggested Citation

  • Pier Bissiri & Stephen Walker, 2012. "Converting information into probability measures with the Kullback–Leibler divergence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(6), pages 1139-1160, December.
    • Handle: RePEc:spr:aistmt:v:64:y:2012:i:6:p:1139-1160
    DOI: 10.1007/s10463-012-0350-4
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    Cited by:

    1. Bissiri, Pier Giovanni & Walker, Stephen G., 2019. "On general Bayesian inference using loss functions," Statistics & Probability Letters, Elsevier, vol. 152(C), pages 89-91.

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