Robust Bayesian synthetic likelihood via a semi-parametric approach

• Published in: Statistics and computing Vol. 30; no. 3; pp. 543 - 557
• Main Authors: An, Ziwen, Nott, David J., Drovandi, Christopher
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2020; Springer Nature B.V
• Subjects: Artificial Intelligence; Bayesian analysis; Computer simulation; Covariance matrix; Mathematics and Statistics; Normal distribution; Normality; Parameter estimation; Parametric statistics; Probability and Statistics in Computer Science; Robustness; Statistical analysis; Statistical Theory and Methods; Statistics; Statistics and Computing/Statistics Programs; Test procedures; Robust estimation; Likelihood-free inference; Copula; Kernel density estimation; Approximate Bayesian computation (ABC); Nonparanormal distribution
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-019-09904-x

Bayesian synthetic likelihood (BSL) is now a well-established method for performing approximate Bayesian parameter estimation for simulation-based models that do not possess a tractable likelihood function. BSL approximates an intractable likelihood function of a carefully chosen summary statistic at a parameter value with a multivariate normal distribution. The mean and covariance matrix of this normal distribution are estimated from independent simulations of the model. Due to the parametric assumption implicit in BSL, it can be preferred to its nonparametric competitor, approximate Bayesian computation, in certain applications where a high-dimensional summary statistic is of interest. However, despite several successful applications of BSL, its widespread use in scientific fields may be hindered by the strong normality assumption. In this paper, we develop a semi-parametric approach to relax this assumption to an extent and maintain the computational advantages of BSL without any additional tuning. We test our new method, semiBSL, on several challenging examples involving simulated and real data and demonstrate that semiBSL can be significantly more robust than BSL and another approach in the literature.