Ensemble Kalman filter based sequential Monte Carlo sampler for sequential Bayesian inference

Jiangqi Wu, Linjie Wen, Peter L Green, Jinglai Li, Simon Maskell

Research output: Contribution to journalArticlepeer-review

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). An advantage of the SMCS method is that, unlike the EnKF method that 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.
Original languageEnglish
Article number20
Number of pages14
JournalStatistics and Computing
Volume32
Issue number1
DOIs
Publication statusPublished - 15 Feb 2022

Bibliographical note

Funding Information:
This work was supported by the NSFC under Grant Number 111771289 and by the EPSRC under Grant Number EP/R018537/1.

Publisher Copyright:
© 2022, The Author(s).

Keywords

  • stat.ME
  • stat.CO
  • Ensemble Kalman filter
  • Parameter estimation
  • Sequential Bayesian inference
  • Sequential Monte Carlo sampler

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