Approximate Bayesian Computation with composite score functions

Erlis Ruli, Nicola Sartori, Laura Ventura

Published 2013-11-28, updated 2014-05-22Version 2

Both Approximate Bayesian Computation (ABC) and composite likelihood methods are useful for Bayesian and frequentist inference when the likelihood function is intractable. We show that composite likelihoods score functions can be fruitfully used as automatic informative summary statistics in ABC in order to obtain accurate approximations to the posterior distribution of the parameter of interest. This is formally motivated by the use of the score function of the full likelihood, and extended to general unbiased estimating functions in complex models. Examples illustrate that the proposed ABC procedure can significantly improve upon usual ABC methods based on ordinary data summaries.