Statistics Seminars: Semi-automatic Approximate Bayesian Computation
25 October 2010 15:15 in CM221
Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but impossible to calculate likelihoods. Approximate Bayesian Computation (ABC) is a method of inference for such models. It replaces calculation of the likelihood by a step which involves simulating artificial data for different parameter values, and comparing summary statistics of the simulated data to summary statistics of the observed data. Here we show how to construct appropriate summary statistics for ABC in a semi-automatic manner. Theoretical results show that, in some sense, optimal summary statistics are the posterior means of the parameters. While these cannot be calculated analytically, we propose using an extra stage of simulation to estimate how the posterior means vary as a function of the data; and then use these estimates of our summary statistics within ABC. Our approach compares with the current norm of the person implementing ABC choosing summary statistics that they think are informative about the parameters. Empirical results, based on two examples from the literature, show that our simulation-based approach to choosing summary statistics can be orders of magnitude more accurate than this alternative.
[Joint work with Dennis Prangle.]
Host: Umberto Picchini
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