Rao-Blackwellized Particle Gibbs Kernels for Smoothing in Jump Markov Nonlinear Models

Jump Markov nonlinear models (JMNMs) characterize a dynamical system by a finite number of presumably nonlinear and possibly non-Gaussian state-space configurations that switch according to a discrete-valued hidden Markov process. In this context, the smoothing problem - the task of estimating fixed points or sequences of hidden variables given all available data -is of key relevance to many objectives of statistical inference, including the estimation of static parameters. The present paper proposes a particle Gibbs with ancestor sampling (PGAS)-based smoother for JMNMs. The design methodology relies on integrating out the discrete process in order to increase the efficiency through Rao-Blackwellization. The experimental evaluation illustrates that the proposed method achieves higher estimation accuracy in less computational time compared to the original PGAS procedure.