Iterative Markov Chain Monte Carlo Computation of Reference Priors and Minimax Risk

TL;DR

This paper introduces an iterative MCMC algorithm for computing reference priors and minimax risk in parametric models, leveraging information theory techniques and providing theoretical analysis and simulations.

Contribution

The paper develops a novel iterative MCMC method based on the Blahut-Arimoto algorithm for reference priors and minimax risk, with rigorous sample complexity analysis.

Findings

Algorithm effectively computes reference priors in exponential families.

Theoretical bounds on sample size for accurate approximation.

Simulation results demonstrate practical applicability.

Abstract

We present an iterative Markov chainMonte Carlo algorithm for computingreference priors and minimax risk forgeneral parametric families. Ourapproach uses MCMC techniques based onthe Blahut-Arimoto algorithm forcomputing channel capacity ininformation theory. We give astatistical analysis of the algorithm,bounding the number of samples requiredfor the stochastic algorithm to closelyapproximate the deterministic algorithmin each iteration. Simulations arepresented for several examples fromexponential families. Although we focuson applications to reference priors andminimax risk, the methods and analysiswe develop are applicable to a muchbroader class of optimization problemsand iterative algorithms.