Stat 321   Monte Carlo Methods     Spring 2004

TTH 11:00-12:15,   New West 104

Website:   www.stat.unc.edu/faculty/cji/321.html

Instructor:   Chuanshu Ji,   New West 201,   962-3917,   cji@email.unc.edu

Office hours:   walk-in service or make appointment via email

Requirement:  

• For grade P:   active participation in class discussion and a short presentation on some of your own work using Monte Carlo methods.
• For grade H:   attempt at all homework assignments and the final project.
• There will be about 5 homework assignments, each including some theoretical/computational problems. The final project topics are to be decided in class. Each student will prepare and give a presentation --- solving some scientific problems via Monte Carlo methods.

Text:  

``Monte Carlo Strategies in Scientific Computing'' (Jun Liu, 2001, Springer) --- a superb book addressing important theoretical and computational issues, also including a broad range of examples in many scientific areas.

References:  

• ``Simulation'' (S. Ross, 3rd edition, 2002, Springer) --- a concise coverage of basics and some modern topics.
• ``Stochastic Simulation'' (B. Ripley, 1987, Wiley) --- a condensed classic, covers many aspects of simulation, including random number generation.
• ``Monte Carlo Statistical Methods'' (C. Robert/ G. Casella, 1999, Springer) --- a nice Bayesian stat oriented book.
• ``Monte Carlo Methods in Bayesian Computation'' (M. Chen/Q. Shao/ J. Ibrahim, 2000, Springer) --- a comprehensive description of Bayesian stat and MCMC.
• ``Monte Carlo Methods in Financial Engineering'' (P. Glasserman, 2003, Springer) --- a new addition to the literature of Monte Carlo methods, with a careful treatment of applications in asset pricing and risk management.
• Several excellent lecture notes and survey papers by Sokal, Aldous/Fill, Gidas, Wilson, et al. (to be given later).

Tentative plan:  

We will cover several chapters of the text, supplemented by materials selected from other references and some of my own sketches.
• Part 1: Basics
  Objectives, pros and cons of Monte Carlo methods; how to generate random variables and stochastic processes; variance reduction; output analysis. These basic issues/techniques will be revisited in Parts 2 and 3.
• Part 2: Markov chain Monte Carlo (MCMC) and related topics
  • the need for MCMC; a long run vs several short runs ...
  • Metropolis dynamics
  • the Gibbs sampler
  • sequential importance sampling (SIS); particle filters; their differences from and connections to MCMC.
  • convergence: theoretical (Markov chain theory and spectra analysis) and practical (diagnostics)
  • some optimization methods: simulated annealing/tempering
  • MCMC software BUGS and other computational issues
  • perfect sampling
• Part 3: Applications
  Examples to be chosen from stat, physics, engineering, bioinformatics/genetics, economics/finance, etc.