Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics
Department of Physical Engineering, Mie University - Mie 514-8507, Japan
Received: 31 August 2014
Accepted: 4 November 2014
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.
PACS: 02.50.Tt – Inference methods / 02.50.Cw – Probability theory / 05.20.-y – Classical statistical mechanics
© EPLA, 2014