Abstract

We introduce a new version of particle filter in which the number of “children” of a particle at a given time has a Poisson distribution. As a result, the number of particles is random and varies with time. An advantage of this scheme is that descendants of different particles can evolve independently. It makes easy to parallelize computations. Moreover, particle filter with Poisson resampling is readily adapted to the case when a hidden process is a continuous time, piecewise deterministic semi-Markov process. We show that the basic techniques of particle MCMC, namely particle independent Metropolis-Hastings, particle Gibbs sampler and its version with ancestor sampling, work under our Poisson resampling scheme. Our version of particle Gibbs sampler is uniformly ergodic under the same assumptions as its standard counterpart. We present simulation results which indicate that our algorithms can compete with the existing methods. Supplemental materials for this article are available online.

摘要

我们引入了一个新版本的粒子过滤器，其中在给定时间粒子的“孩子”的数量具有泊松分布。因此，粒子的数量是随机的，并随时间变化。这种方案的一个优点是不同粒子的后代可以独立进化。它使并行​​化计算变得容易。此外，具有泊松重采样的粒子滤波器很容易适应隐藏过程是连续时间、分段确定性半马尔可夫过程的情况。我们展示了粒子 MCMC 的基本技术，即粒子独立的 Metropolis-Hastings、粒子 Gibbs 采样器及其具有祖先采样的版本，在我们的泊松重采样方案下工作。我们的粒子吉布斯采样器版本在与其标准对应版本相同的假设下是一致遍历的。我们提供的模拟结果表明我们的算法可以与现有方法竞争。本文的补充材料可在线获取。