Open AccessResampled ensemble Kalman inversion for Bayesian parameter estimation with sequential data
Author(s) -
Jiangqi Wu,
Linjie Wen,
Jinglai Li
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2021045
Subject(s) - markov chain monte carlo , computer science , resampling , algorithm , kalman filter , bayesian probability , monte carlo method , particle filter , posterior probability , inversion (geology) , prior probability , importance sampling , mathematical optimization , artificial intelligence , mathematics , statistics , paleontology , structural basin , biology
Many real-world problems require to estimate parameters of interest in a Bayesian framework from data that are collected sequentially in time. Conventional methods to sample the posterior distributions, such as Markov Chain Monte Carlo methods can not efficiently deal with such problems as they do not take advantage of the sequential structure. To this end, the Ensemble Kalman inversion (EnKI), which updates the particles whenever a new collection of data arrive, becomes a popular tool to solve this type of problems. In this work we present a method to improve the performance of EnKI, which removes some particles that significantly deviate from the posterior distribution via a resampling procedure. Specifically we adopt an idea developed in the sequential Monte Carlo sampler, and simplify it to compute an approximate weight function. Finally we use the computed weights to identify and remove those particles seriously deviating from the target distribution. With numerical examples, we demonstrate that, without requiring any additional evaluations of the forward model, the proposed method can improve the performance of standard EnKI in certain class of problems.