A Bayesian parameter estimation and model selection algorithm for strongly nonlinear dynamical systems

A recently proposed general Bayesian inference framework (Bisaillon, Sandhu, Khalil, Poirel,& Sarkar 2013, Khalil, Poirel, & Sarkar 2013, Sandhu, Khalil, Poirel, & Sarkar 2013, Khalil, Sarkar, Adhikari, & Poirel 2013) has been applied for the parameter estimation and model selection of strongly non-Gaussian systems. This Bayesian inference approach necessitates a nonlinear state estimation algorithm for robust statistical inference. The effect of sparse and noisy observational data manifests through strongly non-Gaussian features in the conditional probability density function (pdf) of the system parameters. In this paper, we exploit a Particle filter (PF) algorithm (Chen 2003, Arulampalam, Maskell, Gordon, & Clapp 2002), complemented by the Ensemble Kalman filter (EnKF) (Evensen 2009) for the proposal density (Mandel & Beezley 2007, Mandel & Beezley 2009, Bocquet, Wu, & Pires 2010, Papadakis, Mémin, Cuzol, & Gengembre 2010) for the parameter estimation. Consequently, we investigate the accuracy of this Metropolis-Hastings (M-H) Markov Chain Monte Carlo (MCMC) (Gilks, Spiegelhalter, & Richardson 1996) simulation based parameter estimation algorithm for the Bayesian model selection for a randomly perturbed nonlinear system having multiple equilibrium (fixed) points (Bisaillon, Sandhu, Khalil, Poirel, & Sarkar 2013)