ABSTRACT
Monte Carlo Sampling This chapter presents nonparametric sampling-based algorithms to handle function nonlinearities and multimodal distributions by approximating them via a finite weighted sum of N samples, called particles. With a sufficient number of particles, an approximate distribution can be obtained that is close to the corresponding true distribution. Sampling-based algorithms will be able to handle, for example, temporal models with nonlinear transition and observation functions. They are also useful for Bayesian updates in models involving integrations that cannot be solved analytically or models with both numerical and categorical variables. In this chapter, we cover Markov Chain Monte Carlo (MCMC) sampling algorithms, including Gibbs sampling, the Metropolis-Hastings algorithm, and the particle filter (PF). The PF is especially effective for handling hybrid Dynamic Bayesian Networks (DBNs) containing continuous and discrete variables.
