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

Assignments, exams, grading

The course grade will be based on homework assignments and an individual or small group project and presentation. Assignments will be a combination of programming/computing and traditional paper and pencil work. Students are allowed but not encouraged to typeset answers.

Communication and announcements

Announcements and most course communication will be done on the course page at the NYU Classes site. This site has a class message board that everyone in the class can see. If you have a technical question or comment, please post it there rather than sending an email to the instructor That way everyone has the same information. Please feel free to contribute. You can check your grades here.

Academic integrity (cheating)

The NYU academic integrity policies apply to this class. Students may work together but each student must write her/his answers individually. Students may not hand in work they have copied from another source. Students may not share code.

Schedule (subject to change)

week topics
1 Overview of Monte Carlo, the class and project. Direct sampling methods, mapping, rejection, weighted sampling. Central limit theorem, error bars, and MC computing practice.
2 Variance reduction methods, antithetic variates, control variates. Rare events and importance sampling
3 Markov chain Monte Carlo (MCMC): Markov chains, Perron Frobenius, detailed balance, Metropolis Hastings.
4 Errors in MCMC sampling: ergodic theorem, central limit theorem for Markov chains, auto-covariance, the Einstein Kubo formula for the auto-correlation time and sample variance.
5 Specific applications: Bayesian posterior sampling, interacting particle sysmtems, lattice fields.
6 More MCMC methods: partial resampling (aka Gibbs sampler, aka the heat bath method), exact Langevin methods, choosing proposal distributions, multi-level methods.
7 Some quantitative analysis: spectrum of the generator and spectral gap, calculation for linear Markov chaings.