A multifidelity approximate Bayesian computation with pre-filtering

TL;DR

This paper introduces a multifidelity ABC method with pre-filtering to reduce computational costs, providing theoretical guarantees and practical strategies, validated through numerical experiments and an R package.

Contribution

It proposes a novel hierarchical importance sampling algorithm with pre-filtering for multifidelity ABC, including theoretical analysis and an adaptive SMC implementation.

Findings

The algorithm satisfies posterior concentration properties.

Error bounds and efficiency relationships are characterized.

Numerical experiments demonstrate effectiveness of the approach.

Abstract

Approximate Bayesian Computation (ABC) methods often require extensive simulations, resulting in high computational costs. This paper focuses on multifidelity simulation models and proposes a pre-filtering hierarchical importance sampling algorithm. Under mild assumptions, we theoretically prove that the proposed algorithm satisfies posterior concentration properties, characterize the error upper bound and the relationship between algorithmic efficiency and pre-filtering criteria. Additionally, we provide a practical strategy to assess the suitability of multifidelity models for the proposed method. Finally, we develop a multifidelity ABC sequential Monte Carlo with adaptive pre-filtering strategy. Numerical experiments are used to demonstrate the effectiveness of the proposed approach. We develop an R package that is available at https://github.com/caofff/MAPS