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Multilevel Monte Carlo in approximate Bayesian computation |
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| Authors: | Ajay Jasra Seongil Jo David Nott Christine Shoemaker Raul Tempone |
| Affiliation: | 1. Department of Statistics and Applied Probability and Operations Research Cluster, National University of Singapore, Singapore, Singapore;2. Department of Statistics, Chonbuk National University, Jeonju, Republic of Korea;3. Department of Civil and Environmental Engineering and Operations Research Cluster, National University of Singapore, Singapore, Singapore;4. Center for Uncertainty Quantification in Computational Science and Engineering, King Abdullah University of Science and Technology, Thuwal, Saudi Arabia |
| 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. |
| Keywords: | Approximate Bayesian computation multilevel Monte Carlo sequential Monte Carlo |