Stochastic Processes and Monte Carlo Methods

Catalog description

Conditional probability and expectation, Markov chains, Poisson processes, Continuous-time Markov chains, Monte Carlo methods, Markov chain Monte Carlo. STAT 515 Stochastic Processes and Monte Carlo Methods (3) This course provides an introduction to stochastic processes and Monte Carlo methods. The course covers topics usually covered in a standard introductory course on stochastic processes, including Markov chains of various kinds. It also covers modern Monte Carlo and Markov chain Monte Carlo methods. Simulation and computing are emphasized throughout the course. The course is divided into two parts: the first part (roughly 8 weeks) provides an introduction to stochastic processes, while the latter (roughly 7 weeks) focuses on Monte Carlo methods, including Markov chain Monte Carlo. The first part of the course begins with a review of elementary conditional probability and expectation before covering basic discrete-time Markov chain theory and Poisson processes. The course then provides students with an overview of continuous-time Markov chains and birth-death processes. The second part of the course covers Monte Carlo methods. Starting with basic random variate generation, the course covers classical Monte Carlo methods such as accept-reject and importance sampling before discussing Markov chain Monte Carlo (MCMC) methods, which includes the Metropolis-Hastings and Gibbs sampling algorithms, and Markov chain theory for discrete-time continuous-space Markov chains.