Statistical Models Commons^™

Approximate Bayesian Computation In State Space Models, Gael Martin, Brendan Mccabe, Christian Robert, Worapree Ole Maneesoonthorn

Worapree Ole Maneesoonthorn

A new approach to inference in state space models is proposed, based on approximate Bayesian computation (ABC). ABC avoids evaluation of the likelihood function by matching observed summary statistics with statistics computed from data simulated from the true process; exact inference being feasible only if the statistics are sufficient. With finite sample sufficiency unattainable in the state space setting, we seek asymptotic sufficiency via the maximum likelihood estimator (MLE) of the parameters of an auxiliary model. We prove that this auxiliary model-based approach achieves Bayesian consistency, and that - in a precise limiting sense - the proximity to (asymptotic) sufficiency …