Stochastic Processes and Monte Carlo Methods, spring 2008

This course provides an introduction to stochastic processes and Monte Carlo methods. The course differs from a classical introductory stochastic processes course due to its emphasis on Monte Carlo methods and computing.

The course is divided into two parts: the first 8 weeks provides an introduction to stochastic processes, while the latter 6 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 include the Metropolis-Hastings and Gibbs sampling algorithms. Course requirements include weekly homework assignments --- basic theory problems for the first half and primarily computational/programming assignments through the second half.

Familiarity with basic mathematical statistics and probability (Stat 513 or Stat 414) is assumed as is some familiarity with programming. We will be using the statistical software package R though non-Statistics students are welcome to use a suitable programming language of their choice. The course is a required course for students in the M.S. and Ph.D. programs in statistics, and is recommended as preparation for advanced statistics courses such as Spatial Models (Stat 597).

Policy on academic integrity: All Penn State and Eberly College of Science policies regarding academic integrity apply to this course. See http://www.science.psu.edu/academic/Integrity/index.html for details.