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

翻译：近似贝叶斯计算（ABC）方法通常需要进行大量模拟，导致高昂的计算成本。本文聚焦于多保真度模拟模型，提出了一种预过滤分层重要性采样算法。在温和的假设条件下，我们从理论上证明了所提算法满足后验集中性质，刻画了误差上界以及算法效率与预过滤准则之间的关系。此外，我们提供了一种实用策略来评估多保真度模型对于所提方法的适用性。最后，我们开发了一种具有自适应预过滤策略的多保真度ABC序贯蒙特卡洛方法。数值实验被用于验证所提方法的有效性。我们开发了一个R软件包，可在 https://github.com/caofff/MAPS 获取。