论文标题
集合Kalman滤波器基于顺序贝叶斯推断的顺序蒙特卡洛采样器
Ensemble Kalman filter based Sequential Monte Carlo Sampler for sequential Bayesian inference
论文作者
论文摘要
许多现实世界中的问题需要从贝叶斯框架中估算感兴趣的参数，从及时收集的数据。从后验分布进行采样的常规方法，例如{Markov Chain Monte Carlo}无法有效解决此类问题，因为它们无法利用数据的顺序结构。为此，通常使用新的数据集合时试图更新后验分布的顺序方法通常用于解决这些类型的问题。顺序方法的两个流行选择是集合卡尔曼滤波器（ENKF）和顺序蒙特卡洛采样器（SMC）。尽管ENKF仅计算后验分布的高斯近似值，但SMC可以直接从后部绘制样品。然而，它的性能取决于所使用的内核。在这项工作中，我们提出了一种使用ENKF公式构建SMC内核的方法，并通过数值示例演示了该方法的性能。
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} can not 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.
