Sequential hierarchical Bayesian model and particle filter estimation with two-step RJMCMC resampling

Abstract

Data assimilation (DA) combines numerical model simulations with observed data to obtain the best possible description of a dynamical system and its uncertainty. Incorrect modeling assumptions can lead to filter divergence, making model identification an important issue in the field of DA. Variations in dynamic model structures can result in differences in parameter dimensions, complicating the resampling step in PFs. To meet this challenge, the Sequential Hierarchical Bayesian Model (SHBM) is proposed in this paper, which integrates the evolution model along with observation model from the DA scheme, and the hierarchical parameter model. A two-step resampling method are also proposed to estimate the SHBM: the first step uses the resampling scheme in the bootstrap filter to resample new particles based on weights, which may produce some duplicate particles; the second step utilizes the Reversible Jump Markov Chain Monte Carlo (RJMCMC) methods to draw new particles from the target distribution. This approach ensures particle diversity, with the first step aiming at avoiding particle degeneracy, and the second step intends to prevent the sample impoverishment. The performance in the Advection Equation example and Lorenz 96 example demonstrates the effectiveness of the proposed method.