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Asymptotics of Approximate Bayesian Computation

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SINW01 - Scalable statistical inference

Many statistical applications involve models for which are easy to sample from, but for which it is difficult to evaluate the likelihood. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian inference in such cases. This talk will overview some recent results on the theoretical properties of approximate Bayesian computation which consider the performance of ABC as we get more data. It will cover questions such as: when does the ABC posterior concentrate on the true parameter value? What distribution does the ABC posterior converge to? And what is the frequentist distribution of point-estimates derived using ABC . It will also cover the impact of Monte Carlo error on estimates obtained using ABC , and consider whether, asympotically, it is possible to efficiently estimate parameters using ABC if we have a fixed Monte Carlo sample size.

This is joint work with Wentao Li: https://arxiv.org/abs/1506.03481 and  https://arxiv.org/abs/1609.07135; the talk will also cover work by David Frazier, Martin, Robert and Rousseau: https://arxiv.org/abs/1607.06903

This talk is part of the Isaac Newton Institute Seminar Series series.

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