Conditional maximum-entropy method for selecting prior distributions in Bayesian statistics
arXiv:1409.0228 · doi:10.1209/0295-5075/108/40008
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.
17 pages, 1 figure. Published version