Variance Reduction via Antithetic Markov Chains
James Neufeld, Dale Schuurmans, Michael Bowling · 2015
We present a Monte Carlo integration method, antithetic Markov chain sampling (AMCS), that incorporates local Markov transitions in an un-derlying importance sampler. Like sequential Monte Carlo sampling, the proposed method uses a sequence of Markov transitions to guide the sampling toward influential regions of the in-tegrand (modes). However, AMCS differs in the type of transitions that may be used, the num-ber of Markov chains, and the method of chain termination. In particular, from each point sam-pled from an initial proposal, AMCS collects a sequence of points by simulating two indepen-dent, but antithetic Markov chains, which are terminated by a sample-dependent stopping rule. Such an approach provides greater flexibility for targeting influential areas while eliminating the need to fix the length of the Markov chain a pri-ori. We show that the resulting estimator is un-biased and can reduce variance on peaked multi-modal integrands that challenge current methods. 1