Statistica Sinica 27 (2017), 1595-1618

LEARNING SUMMARY STATISTIC FOR

APPROXIMATE BAYESIAN COMPUTATION

VIA DEEP NEURAL NETWORK

Bai Jiang, Tung-Yu Wu, Charles Zheng and Wing H. Wong

Stanford University

Abstract: Approximate Bayesian Computation (ABC) methods are used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Both the accuracy and computational efficiency of ABC depend on the choice of summary statistic, but outside of special cases where the optimal summary statistics are known, it is unclear which guiding principles can be used to construct effective summary statistics. In this paper we explore the possibility of automating the process of constructing summary statistics by training deep neural networks to predict the parameters from artificially generated data: the resulting summary statistics are approximately posterior means of the parameters. With minimal model-specific tuning, our method constructs summary statistics for the Ising model and the moving-average model, which match or exceed theoretically-motivated summary statistics in terms of the accuracies of the resulting posteriors.

Key words and phrases: Approximate Bayesian computation, deep learning, summary statistic.