MATH-GA.2011-003 Advanced Topics In Numerical Analysis: Monte Carlo Methods
This class concerns the design of Monte Carlo sampling techniques for estimation of averages with respect to high dimensional probability distributions. Standard simulation tools such as importance sampling, Gibbs and Metropolis-Hastings sampling, Langevin dynamics, and hybrid Monte Carlo will be motivated and introduced. We will discuss the qualitative advantages and disadvantages of various schemes. Particular attention will be paid to the major complicating issues like conditioning and rare events along with methods to address them (e.g. tempering, interacting particle methods, and free-energy methods). This class does not cover in-depth mathematical convergence analysis of sampling algorithms.