The pseudo-marginal approach for efficient Monte Carlo computations

Understand

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.