Modern nonparametric approaches to statistical analysis. Infinite dimensional Bayesian models: data analysis, inference and prediction. Models of curves, surfaces, probability distributions, partitions and latent feature spaces; nonparametric density estimation, regression and classification; hierarchical, multivariate and functional data analysis models; theory of estimation in function spaces. Methodology of probabilistic process models: Dirichlet, Gaussian, basis/kernel expansion, splines, wavelets, support vector machines and other local regression models. Interfaces of Bayesian:non-Bayesian methods and additional methodological topics. Prerequisite: Statistical Science 732 and 831.