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.

Bissiri, P., Walker, S. (2012). Converting information into probability measures with the Kullback-Leibler divergence. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 64, 1139-1160 [10.1007/s10463-012-0350-4].

Converting information into probability measures with the Kullback-Leibler divergence

BISSIRI, PIER GIOVANNI
;
2012

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.
Articolo in rivista - Articolo scientifico
Bayesian inference, posterior distribution, loss function, Kullback-Leibler divergence, g-divergence
English
2012
64
1139
1160
none
Bissiri, P., Walker, S. (2012). Converting information into probability measures with the Kullback-Leibler divergence. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 64, 1139-1160 [10.1007/s10463-012-0350-4].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/37006
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