Using nested sampling with Galilean Monte Carlo for model comparison problems in acoustics

Abstract

Nested sampling is increasingly being used to calculate the evidence for competing models in Bayesian model comparison problems arising in acoustics applications. Use of nested sampling offers advantages in robustness over alternative methods of evidence calculation and enables evidence calculation for models with many parameters. The most challenging aspect of implementing nested sampling is sampling from the prior for the parameters constrained by a threshold likelihood value. For models with just a few parameters, sampling from the constrained prior can be accomplished with a simple Monte Carlo algorithm implementing a random walk, however, this simple method is inefficient and fails as the number of model parameters increases. John Skilling, the originator of nested sampling, has proposed the "Galilean" Monte Carlo method for efficiently sampling from the constrained prior when there are many parameters. Unlike the random walk method, the Galilean Monte Carlo method moves samples with a vector velocity, reflecting them from the likelihood constraint surface when necessary. This directed sampling gives the method its greater efficiency. In this paper we discuss our experience in implementing Galilean Monte Carlo in nested sampling and compare Galilean and random walk Monte Carlo for a model comparison problem in room acoustics.