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Paper No. 12-04

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FJ Rubio and AM Johansen

On Maximum Intractable Likelihood Estimation

Date: March 2012

Abstract: Approximate Bayesian Computation (ABC) may be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Considering the first step as an explicit approximation of the likelihood allows, also, maximum-likelihood (or maximum-a-posteriori) inference to be conducted, approximately, using essentially the same techniques. Such an approach is developed here and the convergence of this class of algorithms is characterised theoretically. The use of non-sufficient summary statistics is considered. Applying the proposed method to three problems demonstrates good performance. The proposed approach provides an alternative for approximating the maximum likelihood estimator (MLE) in complex scenarios.

Keywords: Approximate Bayesian Computation; Density Estimation; Maximum Likelihood Estimation; Monte Carlo Methods.