Optimal scaling of the independence sampler: Theory and Practice

TL;DR

This paper investigates the optimal scaling of the independence sampler in Bayesian data augmentation, providing guidelines for its use and demonstrating their effectiveness in epidemic models.

Contribution

It offers new theoretical guidelines for optimizing the independence sampler's performance in Bayesian data augmentation, extending beyond idealized models.

Findings

Guidelines for optimal proportion of augmented data to update

Theoretical results applicable to product densities

Effective in epidemic modeling examples

Abstract

The independence sampler is one of the most commonly used MCMC algorithms usually as a component of a Metropolis-within-Gibbs algorithm. The common focus for the independence sampler is on the choice of proposal distribution to obtain an as high as possible acceptance rate. In this paper we have a somewhat different focus concentrating on the use of the independence sampler for updating augmented data in a Bayesian framework where a natural proposal distribution for the independence sampler exists. Thus we concentrate on the proportion of the augmented data to update to optimise the independence sampler. Generic guidelines for optimising the independence sampler are obtained for independent and identically distributed product densities mirroring findings for the random walk Metropolis algorithm. The generic guidelines are shown to be informative beyond the narrow confines of idealised product densities in two epidemic examples.