Monte Carlo Methods, MATH-GA.394.001, Spring, 2017

Class notes

• Week1.pdf
• Week2.pdf

Project suggestions

• possibleProjects.pdf

Basic books

Each of these books has great descriptions of the material from the early weeks. Many of thm are out of print, but used copies are so cheap and so high quality that it makes sense to buy them. One place, which I mention without endorsing, is Abe books.

• Monte Carlo Methods, Hammersley, J M Handscomb, D C
  This is the original book on Monte Carlo methods. Much of the material is dated, but much of the dated material should be known better than it is.
• Monte Carlo Methods, Volume 1: Basics, Malvin Kalos, Paula Whitlock
  A great gentle but consice and insightful introduction to Monte Carlo, particularly for physical sciences. The book is more mathematical than it pretends to be.
• Monte Carlo theory, methods and examples, Art B. Owen
  Still high quality and clear, but with more background and modern detail than the previous two. Lots of careful and helpful practical examples from statistics. Available only online, so far.

Specialized material

• Week 1
  • Chapter 1 of this set of notes is a good description of modern pseudo-random number generators, how they work and how we test them.
  • Bayesian statistics is sometimes called undertainty quantification, or UQ. There is a research group at MIT devoted to this.
  • Uncertainty quantification for parameter estimation in biological applications.
• Week 2
  • Importance Sampling: A Review, Surya T. Tokdar and Robert E. Kass A statisticians' quick survey of importance sampling ideas, the relationship between the basics and more advanced developments such as adaptively finding importance functions and sequential importance sampling.
  • Simulation E±ciency and an Introduction to Variance Reduction Methods, Martin Haugh Class notes on variance reduction methods from the point of view of operations research and Monte Carlo estimation in finance (derivative pricing).