Converting information into probability measures with the Kullback–Leibler divergence

Pier Bissiri () and Stephen Walker ()

Annals of the Institute of Statistical Mathematics, 2012, vol. 64, issue 6, 1139-1160

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

Keywords: Bayesian inference; Posterior distribution; Loss function; Kullback–Leibler divergence; g-divergence (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10463-012-0350-4

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