STAT 251b / STAT 551b Stochastic Processes
Introduction to the study of random processes, including Markov chains, Markov random fields, martingales, random walks, Brownian motion, and diffusions. Techniques in probability, such as coupling and large deviations. Applications chosen from image reconstruction, Bayesian statistics, finance, probabilistic analysis of algorithms, and genetics and evolution.
STAT 679a High-Dimensional Statistical Estimation
In this course we will review the recent advances in high-dimensional statistics. We will cover concepts in empirical process theory, concentration of measure, and random matrix theory in the context of understanding the statistical properties of high-dimensional estimation methods. In this discussion we will also overview the computational constraints that are involved with solving high-dimensional problems and touch upon concepts in convex optimization and online learning.