Ensemble Kalman filter based Sequential Monte Carlo Sampler for sequential Bayesian inference

TL;DR

This paper introduces a novel approach combining the Ensemble Kalman filter with Sequential Monte Carlo sampling to improve Bayesian inference from sequential data, leveraging EnKF to enhance SMCS kernel construction.

Contribution

The paper proposes a new method that uses EnKF to construct kernels for SMCS, enabling more efficient sequential Bayesian inference.

Findings

The proposed method outperforms traditional SMCS in numerical experiments.

EnKF-based kernels improve sampling efficiency and accuracy.

The approach effectively handles sequential data in Bayesian inference.

Abstract

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.