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Abstract:
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This paper discusses an example of Bayesian statistical inference and its relationship with entropy, the Kullback-Leibler divergence, and Fisher's information. Using an example from science it shows how the information gain in Bayesian updating can be measured using the Kullback-Leibler divergence or cross entropy, change in entropy, and Fisher's information. This example discusses the relationship between these measurements and provides a geometric interpretation for Riemannian distances and pseudo-distances. A numeric example is developed and detailed results are discussed under information theory and statistical point of views by comparing related quantities. Bayesian inference results and theory are interpreted using information concepts, entropy and statistical measurements, finally some conclusions are drawn regarding the information gain and relationship with other statistical procedures.
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