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.
- Approximate Bayesian computation
- multilevel Monte Carlo
- sequential Monte Carlo
ASJC Scopus subject areas
- Applied Mathematics
- Statistics and Probability
- Statistics, Probability and Uncertainty