We consider weighted particle systems in which new generations are re-sampled from current particles with probabilities proportional to their weights. This covers a broad class of sequential Monte Carlo methods, widely used in applied statistics. We consider the genealogical tree embedded into such particle system. When the time is reversed, the particle system induces a partition valued family of processes (partitions on the leaves of the genealogical tree). Our aim here is to give a counterexample to a well known formula describing the transition probabilities of this process.

翻译：我们考虑加权粒子系统，其中新一代粒子依据当前粒子的权重成比例的概率进行重采样。这涵盖了广泛应用于应用统计学的序贯蒙特卡洛方法的一大类。我们研究嵌入此类粒子系统中的谱系树。当时间反转时，该粒子系统导出一个以划分取值的随机过程族（对应于谱系树叶子上的划分）。本文旨在给出一个反例，反驳该过程转移概率的著名公式。