The pseudo-marginal approach for efficient Monte Carlo computations

TL;DR

This paper presents a flexible MCMC algorithm based on the pseudo-marginal approach, enabling efficient stochastic simulation with proven convergence properties and promising empirical performance.

Contribution

It extends the pseudo-marginal method to a broader class of algorithms, demonstrating their theoretical convergence and empirical effectiveness.

Findings

The algorithm shares the same stationary distribution as the idealized marginal method.

Theoretical convergence properties are established.

Numerical examples show promising empirical results.

Abstract

We introduce a powerful and flexible MCMC algorithm for stochastic simulation. The method builds on a pseudo-marginal method originally introduced in [Genetics 164 (2003) 1139--1160], showing how algorithms which are approximations to an idealized marginal algorithm, can share the same marginal stationary distribution as the idealized method. Theoretical results are given describing the convergence properties of the proposed method, and simple numerical examples are given to illustrate the promising empirical characteristics of the technique. Interesting comparisons with a more obvious, but inexact, Monte Carlo approximation to the marginal algorithm, are also given.