Summary Statistics for ABC

• Activity Number: 230
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Dennis Prangle*+ and Paul Fearnhead
• Companies: Lancaster University and Lancaster University
• Keywords: ABC ; Simulation ; Queues ; Systems biology

Abstract

Many modern statistical applications involve inference for complex stochastic models, where it is easy to simulate from the models, but difficult or 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. The results are based on an approximation to the posterior distribution, whose quality depends crucially on the summary statistics. The question of how best to choose these has been an open problem in the literature, with most applications using an ad-hoc choice. This talk describes a generic method to provide summary statistics and presents results showing that it outperforms previous choices in a range of applications including queueing, quantile distributions and systems biology.