The use of a single pseudo-sample in approximate Bayesian computation
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We analyze the computational efficiency of approximate Bayesian computation (ABC), which approximates a likelihood function by drawing pseudo-samples from the associated model. For the rejection sampling version of ABC, it is known that multiple pseudo-samples cannot substantially increase (and can substantially decrease) the efficiency of the algorithm as compared to employing a high-variance estimate based on a single pseudo-sample. We show that this conclusion also holds for a Markov chain Monte Carlo version of ABC, implying that it is unnecessary to tune the number of pseudo-samples used in ABC-MCMC. This conclusion is in contrast to particle MCMC methods, for which increasing the number of particles can provide large gains in computational efficiency.
KeywordsMarkov Chain Markov Chain Monte Carlo Asymptotic Variance Markov Chain Monte Carlo Method Target Distribution
The authors thank Alex Thiery for his careful reading of an earlier draft, as well as Pierre Jacob, Rémi Bardenet, Christophe Andrieu, Matti Vihola, Christian Robert, and Arnaud Doucet for useful discussions. This research was supported in part by U.S. National Science Foundation grants 1461435, DMS-1209103, and DMS-1406599, by DARPA under Grant No. FA8750-14-2-0117, by ARO under Grant No. W911NF-15-1-0172, and by NSERC.
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