We study weighted particle systems in which new generations are resampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo (SMC) methods, widely-used in applied statistics and cognate disciplines. We consider the genealogical tree embedded into such particle systems, and identify conditions, as well as an appropriate time-scaling, under which they converge to the Kingman n-coalescent in the infinite system size limit in the sense of finite-dimensional distributions. Thus, the tractable n-coalescent can be used to predict the shape and size of SMC genealogies, as we illustrate by characterising the limiting mean and variance of the tree height. SMC genealogies are known to be connected to algorithm performance, so that our results are likely to have applications in the design of new methods as well. Our conditions for convergence are strong, but we show by simulation that they do not appear to be necessary.

翻译：我们研究加权粒子系统,使新一代人从目前的粒子中重新采样,其概率与其重量成比例。这涵盖了广泛的一系列相继的蒙特卡洛(SMC)方法,广泛用于应用统计和古代学科。我们考虑嵌入这种粒子系统中的基因树,并找出条件和适当的时间缩放,根据这些条件和时间缩放,它们与Kingman n-coights相融合,在有限维度分布感的无限系统尺寸限制下,它们具有一定的趋同性。因此,可以使用可移动的 n-coane 来预测SMC 基因库的形状和大小,正如我们通过描述树高的有限平均值和差异来说明的那样。我们知道SMC 基因圈与算法的性能有联系,因此我们的结果有可能在设计新方法时也有应用。我们的趋同性条件是很强的,但我们通过模拟来显示它们似乎没有必要。