Approximate Bayesian computation using auxiliary model based estimates

We present a novel approach for developing summary statistics for use in approximate Bayesian computation (ABC) algorithms using indirect infer- ence. We embed this approach within a sequential Monte Carlo algorithm that is completely adaptive. This methodological development was motivated by an application involving data on macroparasite population evolution modelled with a trivariate Markov process. The main objective of the analysis is to compare inferences on the Markov process when considering two di®erent indirect mod- els. The two indirect models are based on a Beta-Binomial model and a three component mixture of Binomials, with the former providing a better ¯t to the observed data.