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Multilevel Monte Carlo in Approximate Bayesian Computation

Ajay Jasra, Department of Statistics & Applied Probability & Operations Research Cluster, National University of Singapore, Singapore, 117546, SG. staja@nus.edu.sg

Seongil Jo, Department of Statistics & Applied Probability & Operations Research Cluster, National University of Singapore, Singapore, 117546, SG. joseongil@gmail.com

David Nott, Department of Statistics & Applied Probability & Operations Research Cluster, National University of Singapore, Singapore, 117546, SG. standj@nus.edu.sg

Christine Shoemaker, Department of Civil & Environmental Engineering & Operations Research Cluster, National University of Singapore, Singapore, 119260, SG. shoemaker@nus.edu.sg

Raul Tempone, Center for Uncertainty Quantification in Computational Science & Engineering, King Abdullah University of Science and Technology, Thuwal, 23955-6900, KSA. raul.tempone@kaust.edu.sa

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ABSTRACT

In the following article we consider approximate Bayesian computation (ABC) inference. We introduce a method for numerically approximating ABC posteriors using the multilevel Monte Carlo (MLMC). A sequential Monte Carlo version of the approach is developed and it is shown under some assumptions that for a given level of mean square error, this method for ABC has a lower cost than i.i.d. sampling from the most accurate ABC approximation. Several numerical examples are given.

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