Bayesian experimental design for models with intractable likelihoods

Abstract

In this paper we present a methodology for designing experiments for efficiently estimating the parameters of models with computationally intractable likelihoods. The approach combines a commonly used methodology for robust experimental design, based on Markov chain Monte Carlo sampling, with approximate Bayesian computation (ABC) to ensure that no likelihood evaluations are required. The utility function considered for precise parameter estimation is based upon the concentration of the ABC posterior distribution, which we form efficiently via ABC rejection based on pre-computed model simulations. Our focus is on stochastic models and, in particular, we investigate the methodology on Markov process models for epidemics and macroparasite population evolution.