Bayesian estimation of nonlinear state-space models.

Summary This thesis introduces two new classes of nonlinear state-space models and establishes algorithms for their estimation in a Bayesian framework. The first class is a multivariate generalization of Markov regime-switching models in the sense that it allows the incorporation of several latent variables. This methodology is illustrated by an application in finance where a multivariate stochastic volatility model with several discrete latent variables is estimated on portfolio returns. The second class, called quartic state-space models, allows the study of the dynamics of bimodal laws in a very general framework. An illustration on a longitudinal basis of gross domestic products shows the evolution of the two modes of world income distribution and characterizes the convergence between different groups of countries.