Spring 2021 STAT 31511

Course: STAT 31511=CAAM 31511

Title: Monte Carlo Simulation

Instructor(s): Daniel Sanz-Alonso

Teaching Assistant(s): Yuming Chen

Class Schedule: Section 1: TR 11:20 AM–12:40 PM (Remote)

Description: This class primarily concerns the design and analysis of Monte Carlo sampling techniques for the estimation of averages with respect to high dimensional probability distributions. Standard simulation tools such as importance sampling, Metropolis-Hastings, Langevin dynamics, and hybrid Monte Carlo will be introduced along with basic theoretical concepts regarding their convergence to equilibrium. The class will explore applications of these methods in Bayesian statistics and machine learning as well as to other simulation problems arising in the physical and biological sciences. Particular attention will be paid to the major complicating issues like conditioning (with analogies to optimization) and rare events and methods to address them.

Prerequisite(s): Multivariate calculus and linear algebra; elementary knowledge of ordinary differential equations.