Sequential Monte Carlo methods for parameter estimation in nonlinear state-space models

Stochastic nonlinear state-space models (SSMs) are prototypical mathematical models in geoscience. Estimating unknown parameters in nonlinear SSMs is an important issue for environmental modeling. In this paper, we present two recently developed methods that are based on the sequential Monte Carlo (SMC) method for parameter estimation in nonlinear SSMs. The first method, which belongs to classical statistics, is the SMC-based maximum likelihood estimation. The second method, belonging to Bayesian statistics, is Particle Markov Chain Monte Carlo (PMCMC). With a low-dimensional nonlinear SSM, the implementations of the two methods are demonstrated. It is concluded that these SMC-based parameter estimation methods are applicable to environmental modeling and geoscience.

► Two new methods for parameter estimation in nonlinear state-space model are presented.
► The two methods belong to classic statistics and Bayesian statistics, respectively.
► Numerical experiments for a prototypic model in Geoscience were given.