Leitura do Dia - Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation

Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation

Paul Fearnhead and Dennis Prangle

Lancaster University, UK

[Read before The Royal Statistical Society at a meeting organized by the Research Section on

Wednesday, December 14th, 2011, Professor D. M. Titterington in the Chair ]

Summary. 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 with summary statistics of the observed data. Here we show how to construct appropriate summary statistics for ABC in a semi-automatic manner.We aim for summary statistics which will enable inference about certain parameters of interest to be as accurate as possible. Theoretical results show that optimal summary statistics are the posterior means of the parameters. Although these cannot be calculated analytically, we use an extra stage of simulation to estimate how the posterior means vary as a function of the data; and we then use these estimates of our summary statistics within ABC. Empirical results show that our approach is a robust method for choosing summary statistics that can result in substantially more accurate ABC analyses than the ad hoc choices of summary statistics that have been proposed in the literature.We also demonstrate advantages over two alternative methods of simulation-based inference.

Keywords: Indirect inference; Likelihood-free inference; Markov chain Monte Carlo methods;

Simulation; Stochastic kinetic networks