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Asymptotics for ABC algorithms

Presented by: 
Judith Rousseau University of Oxford, Université Paris-Dauphine
Date: 
Thursday 18th January 2018 - 14:00 to 14:45
Venue: 
INI Seminar Room 1
Abstract: 
Approximate Bayesoan Computation algorithms (ABC) are used in cases where the likelihood is intractable. To simulate from the (approximate) posterior distribution a possiblity is to sample new data from the model and check is these new data are close in some sense to the true data. The output of this algorithms thus depends on how we define the notion of closeness, which is based on a choice of summary statistics and on a threshold. Inthis work we study the behaviour of the algorithm under the assumption that the summary statistics are concentrating on some deterministic quantity and characterize the asymptotic behaviour of the resulting approximate posterior distribution in terms of the threshold and the rate of concentration of the summary statistics. The case of misspecified models is also treated where we show that surprising asymptotic behaviour appears.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons