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Title: PABC: Probably approximate Bayesian computation Authors:  James Ridgway - CFM (France) [presenting]
Abstract: Approximate Bayesian computation (ABC) is a widely used inference method in Bayesian statistics to bypass the point-wise computation of the likelihood. We develop theoretical bounds for the distance between the statistics used in ABC. We show that some versions of ABC are inherently robust to misspecification. The bounds are given in the form of oracle inequalities for a finite sample size. The dependence on the dimension of the parameter space and the number of statistics is made explicit. We apply our theoretical results to given prior distributions and data generating processes, including a non-parametric regression model. We will also show how to use a sequential Monte Carlo sampler (SMC) to sample from the pseudo-posterior, improving upon the state-of-the-art samplers.