We develop a Python source code of Expectation-Maximization (EM)-based algorithms for estimating error covariances in Lorenz-63 state-space models. We investigate to create stochastic (approximation) EM algorithms using Conditional Particle Filtering-Backward Simulation (CPFBS-S(A)EM). This approach is compared to other EM methods using Extended Kalman smoother (EKS-EM), Ensemble Kalman smoother (EnKS-EM), a standard Particle smoother (PFBS-S(A)EM), and Conditional particle filtering-Ancestor sampling smoother (CPFAS-S(A)EM). We show their performances in terms of estimating log likelihood function, errors covariances. We also compare the reconstruction quality (RMSE, coverage probability) between CPFBS and CPFAS smoothers.
This source code was used to produce numerical results in the manuscript Comparison of simulation-based algorithms for parameter estimation and state reconstruction in nonlinear state-space models published in Discrete and Continuous Dynamical Systems Series S (DOI: 10.3934/dcdss.2022054).
Authors: T. T. T. Chau (trang.chau@lsce.ipsl.fr, thi.tuyet.trang.chau@gmail.com), P. Ailliot (pierre.ailliot@univ-brest.fr), V. Monbet (valerie.monbet@univ-rennes1.fr), and P. Tandeo ( pierre.tandeo@imt-atlantique.fr)