Multilevel Monte Carlo in Approximate Bayesian Computation
Ajay Jasra, Seongil Jo, David Nott, Christine Shoemaker, Raul Tempone
TL;DR
This paper introduces a multilevel Monte Carlo method for approximate Bayesian computation, significantly reducing computational cost while maintaining accuracy, and demonstrates its effectiveness through numerical examples.
Contribution
It develops a novel MLMC approach for ABC inference, including a sequential Monte Carlo implementation, improving efficiency over traditional sampling methods.
Findings
Lower computational cost for a given mean square error
Effective in various numerical examples
Outperforms i.i.d. sampling in accuracy-cost trade-off
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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Taxonomy
TopicsMarkov Chains and Monte Carlo Methods · Gaussian Processes and Bayesian Inference · Statistical Methods and Bayesian Inference