Bayesian Learning in Nonlinear State-Space Models

We describe Bayesian learning in nonlinear state-space models (NSSMs). NSSMs are a general method for the probabilistic modelling of sequences and time-series. They take the form of iterated maps on continuous state-spaces, and can have either discrete or continuous valued output functions. They are generalizations of the more well known state-space models such as Hidden Markov models (HMMs), and Linear-Gaussian statespace models (LSSMs). In this paper, we describe the problems of Bayesian learning and inference and in NSSMs. We present an MCMC methods of sampling from the posterior of the parameters given observed data. This method involves the iteration of a parameter estimation step given known statespace trajectories, and state-space inference step given known parameter values. It bears a superficial similarity to the EM algorithm, can be compared with other MCMC methods such as Gibbs sampling.