Art and science of building advanced probabilistic models. EM and stochastic based algorithms will be discussed in detail for inference and prediction. Topics include mixture models and latent variable models, i.e. hidden Markov models. Review of discrete and continuous multivariate distributions used in building graphical models, tools of linear algebra and probability calculus. Aspects of Monte Carlo methodology and related dynamical modeling theory and algorithms/computation. Understanding why and when models and methods work or break will be a focus. Prerequisite: Statistical Science 602L or 702L, and Statistical Science 532.