N Friel, A Mira and CJ Oates
Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods
Abstract: Many popular statistical models for complex phenomena are intractable, in the sense that the likelihood function cannot easily be evaluated, even up to proportionality. Bayesian estimation in this setting remains challenging, with a lack of computational methodology to fully exploit modern processing capabilities. In this paper we introduce novel control variates for intractable likelihoods that can reduce the Monte Carlo variance of Bayesian estimators, in some cases dramatically. We prove that these control variates are well-defined, provide a positive variance reduction and derive optimal tuning parameters that are targeted at optimising this variance reduction. Moreover, the methodology is highly parallelisable and offers a route to exploit multi-core processing architectures for Bayesian computation. Results presented on the Ising model, exponential random graphs and nonlinear stochastic di_erential equations support our theoretical findings.
Keywords: Control variates, zero variance, MCMC, parallel computing.