Approximate Bayesian Computation with composite score functions

Abstract

Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference, respectively, when the likelihood function is intractable. We propose to use composite likelihood score functions as summary statistics in ABC in order to obtain accurate approximations to the posterior distribution. This is motivated by the use of the score function of the full likelihood, and extended to general unbiased estimating functions in complex models. Moreover, we show that if the composite score is suitably standardised, the resulting ABC procedure is invariant to reparameterisations and automatically adjusts the curvature of the composite likelihood, and of the corresponding posterior distribution. The method is illustrated through examples with simulated data, and an application to modelling of spatial extreme rainfall data is discussed.

Statistics and Computing (final version)

References in corpus (6)

• Expectation Propagation for approximate Bayesian inference
• Statistical Modeling of Spatial Extremes
• Stationary max-stable fields associated to negative definite functions
• On spatial extremes: with application to a rainfall problem
• Bayesian Indirect Inference Using a Parametric Auxiliary Model
• ML, PL, QL in Markov chain models

Cited by in corpus (5)

• Objective Bayesian inference with proper scoring rules
• Robust approximate Bayesian inference
• Approximate Bayesian Computation by Modelling Summary Statistics in a Quasi-likelihood Framework
• ABC model selection for spatial extremes models applied to South Australian maximum temperature data
• Generalized Bayesian Likelihood-Free Inference