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

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.

Automated summary

Many real-world problems require estimation of parameters of interest in a Bayesian framework from sequentially collected data. Conventional methods for sampling from posterior distributions do not efficiently address these problems as they do not consider the sequential structure of the data. Therefore, sequential methods like EnKF and SMCS are often used to update the posterior distribution and solve such problems.