Many real-world problems require one to estimate parameters of interest, in a Bayesian framework, from data that are collected sequentially in time. Conventional methods for sampling from posterior distributions, such as Markov chain Monte Carlo cannot efficiently address such problems as they do not take advantage of the data’s sequential structure. To this end, sequential methods which seek to update the posterior distribution whenever a new collection of data become available are often used to solve these types of problems. Two popular choices of sequential method are the ensemble Kalman filter (EnKF) and the sequential Monte Carlo sampler (SMCS). While EnKF only computes a Gaussian approximation of the posterior distribution, SMCS can draw samples directly from the posterior. Its performance, however, depends critically upon the kernels that are used. In this work, we present a method that constructs the kernels of SMCS using an EnKF formulation, and we demonstrate the performance of the method with numerical examples.

许多现实世界的问题需要一个人在贝叶斯框架中从按时间顺序收集的数据中估计感兴趣的参数。从后验分布中采样的传统方法，例如马尔可夫链蒙特卡罗，不能有效地解决这些问题，因为它们没有利用数据的顺序结构。为此，每当有新的数据集合可用时，寻求更新后验分布的顺序方法通常用于解决这些类型的问题。两种流行的顺序方法选择是集成卡尔曼滤波器 (EnKF) 和顺序蒙特卡罗采样器 (SMCS)。虽然 EnKF 只计算后验分布的高斯近似，但 SMCS 可以直接从后验中抽取样本。然而，它的表现，严重依赖于所使用的内核。在这项工作中，我们提出了一种使用 EnKF 公式构建 SMCS 内核的方法，并通过数值示例证明了该方法的性能。