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. Bayesian estimation in this setting remains challenging, with a lack of computa- tional methodology to fully exploit modern processing capabilities. In this paper we introduce novel control variates for intractable likelihoods that can dramati- cally reduce the Monte Carlo variance of Bayesian estimators. We prove that our control variates are well-defined and provide a positive variance reduction. Fur- thermore, we show how to optimise these control variates for variance reduction. The methodology is highly parallel and offers a route to exploit multi-core pro- cessing architectures that complements recent research in this direction. Indeed, our work shows that it may not be necessary to parallelise the sampling process itself in order to harness the potential of massively multi-core architectures. Simu- lation results presented on the Ising model, exponential random graph models and non-linear stochastic differential equation models support our theoretical findings.