Marginal Likelihood Computation via Arrogance Sampling

TL;DR

This paper introduces 'arrogance sampling,' a non-parametric importance sampling method for estimating marginal likelihoods and Bayes factors in Bayesian models, offering a practical alternative to traditional estimators.

Contribution

The paper presents a novel importance sampling technique called arrogance sampling for efficient marginal likelihood estimation, implemented in an open-source R package.

Findings

Effective estimation of marginal likelihoods using arrogance sampling.

Provides a practical alternative to the harmonic mean estimator.

Implemented in the open-source R package margLikArrogance.

Abstract

This paper describes a method for estimating the marginal likelihood or Bayes factors of Bayesian models using non-parametric importance sampling ("arrogance sampling"). This method can also be used to compute the normalizing constant of probability distributions. Because the required inputs are samples from the distribution to be normalized and the scaled density at those samples, this method may be a convenient replacement for the harmonic mean estimator. The method has been implemented in the open source R package margLikArrogance.