Target Density Normalization for Markov Chain Monte Carlo Algorithms

TL;DR

This paper evaluates methods for estimating the normalization constant of target densities in Markov Chain Monte Carlo algorithms, favoring the sample mean approach on reduced support regions based on numerical tests.

Contribution

It introduces and compares techniques for normalization integral estimation in MCMC, providing practical guidelines and demonstrating the effectiveness of the sample mean method.

Findings

Sample mean algorithm performs best on reduced support regions

Harmonic mean and Laplace methods are less reliable

Guidelines for implementation are provided

Abstract

Techniques for evaluating the normalization integral of the target density for Markov Chain Monte Carlo algorithms are described and tested numerically. It is assumed that the Markov Chain algorithm has converged to the target distribution and produced a set of samples from the density. These are used to evaluate sample mean, harmonic mean and Laplace algorithms for the calculation of the integral of the target density. A clear preference for the sample mean algorithm applied to a reduced support region is found, and guidelines are given for implementation.