We propose a sequential Monte Carlo (SMC) method to efficiently and accurately compute cut-Bayesian posterior quantities of interest, variations of standard Bayesian approaches constructed primarily to account for model misspecification. We prove finite sample concentration bounds for estimators derived from the proposed method and apply these results to a realistic setting where a computer model is misspecified. Two theoretically justified variations are presented for making the sequential Monte Carlo estimator more computationally efficient, based on linear tempering and finding suitable permutations of initial parameter draws. We then illustrate the SMC method for inference in a modular chemical reactor example that includes submodels for reaction kinetics, turbulence, mass transfer, and diffusion. The samples obtained are commensurate with a direct-sampling approach that consists of running multiple Markov chains, with computational efficiency gains using the SMC method. Overall, the SMC method presented yields a novel, rigorous approach to computing with cut-Bayesian posterior distributions.

翻译：本文提出一种序贯蒙特卡洛方法，用于高效精确地计算割裂贝叶斯后验中的目标量；该方法是对标准贝叶斯方法的改进，主要旨在处理模型误设定问题。我们证明了所提方法所得估计量的有限样本集中界，并将这些结果应用于计算机模型存在误设定的实际场景。基于线性退火和寻找初始参数抽取的合适排列，我们提出了两种理论可证的改进方案，以提升序贯蒙特卡洛估计量的计算效率。随后，我们在包含反应动力学、湍流、传质和扩散子模型的模块化化学反应器示例中，演示了该序贯蒙特卡洛方法用于推断的过程。所得样本与通过运行多条马尔可夫链的直接抽样方法结果一致，且序贯蒙特卡洛方法具有更高的计算效率。总体而言，本文提出的序贯蒙特卡洛方法为割裂贝叶斯后验分布的计算提供了一种新颖且严谨的途径。