We provide a framework which admits a number of ``marginal'' sequential Monte Carlo (SMC) algorithms as particular cases -- including the marginal particle filter [Klaas et al., 2005, in: Proceedings of Uncertainty in Artificial Intelligence, pp. 308--315], , the independent particle filter [Lin et al., 2005, Journal of the American Statistical Association 100, pp. 1412--1421] and linear-cost Approximate Bayesian Computation SMC [Sisson et al., 2007, Proceedings of the National Academy of Sciences (USA) 104, pp. 1760--1765.]. We provide conditions under which such algorithms obey laws of large numbers and central limit theorems and provide some further asymptotic characterizations. Finally, it is shown that the asymptotic variance of a class of estimators associated with certain marginal SMC algorithms is never greater than that of the estimators provided by a standard SMC algorithm using the same proposal distributions.

翻译：本文提出一个框架，将多种“边缘化”序贯蒙特卡洛（SMC）算法视为特例——包括边缘粒子滤波器[Klaas等，2005，见：《不确定性人工智能会议论文集》，第308–315页]、独立粒子滤波器[Lin等，2005，《美国统计协会杂志》第100卷，第1412–1421页]以及线性成本近似贝叶斯计算SMC[Sisson等，2007，《美国国家科学院院刊》（美国）第104卷，第1760–1765页]。我们给出了此类算法满足大数定律和中心极限定理的条件，并提供了进一步渐近特征刻画。最后证明：对于使用相同提议分布的标准SMC算法，与之相关的某类边际SMC算法估计量的渐近方差始终不大于前者。