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arXiv · 1409.0228

Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics

Sumiyoshi Abe
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Abstract

The conditional maximum-entropy method (abbreviated here as C-MaxEnt) is formulated for selecting prior probability distributions in Bayesian statistics for parameter estimation. This method is inspired by a statistical-mechanical approach to systems governed by dynamics with largely-separated time scales and is based on three key concepts: conjugate pairs of variables, dimensionless integration measures with coarse-graining factors and partial maximization of the joint entropy. The method enables one to calculate a prior purely from a likelihood in a simple way. It is shown in particular how it not only yields Jeffreys's rules but also reveals new structures hidden behind them.

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Sumiyoshi Abe. 2014-11-26. Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics. https://doi.org/10.1209/0295-5075%2F108%2F40008

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