Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models

Abstract

A computationally simple approach to inference in state space models is proposed, using approximate Bayesian computation (ABC). ABC avoids evaluation of an intractable likelihood by matching summary statistics for the observed data with statistics computed from data simulated from the true process, based on parameter draws from the prior. Draws that produce a “match” between observed and simulated summaries are retained, and used to estimate the inaccessible posterior. With no reduction to a low-dimensional set ofsufficient statistics being possible in the state space setting, we define the summaries as the maximum of an auxiliary likelihood function, and thereby exploit the asymptotic suffi..