The use of a single pseudo-sample in approximate Bayesian computation |
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Authors: | Luke Bornn Natesh S Pillai Aaron Smith Dawn Woodard |
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Institution: | 1.Department of Statistics and Actuarial Science,Simon Fraser University,Burnaby,Canada;2.Department of Statistics,Harvard University,Cambridge,USA;3.Department of Mathematics and Statistics,University of Ottawa,Ottawa,Canada;4.School of Operations Research and Information Engineering,Cornell University,Ithaca,USA |
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Abstract: | 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. |
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