STATS 102C: Introduction to Monte Carlo Methods

This course provides students with a solid foundation in probability, statistics, and computational methods for simulating and analyzing complex systems. Students will learn techniques for generating random variables, apply Monte Carlo methods for integration and variance reduction, and develop an understanding of Markov chains and their convergence properties. The course further introduces Markov Chain Monte Carlo (MCMC) methods, including the Metropolis–Hastings algorithm and Gibbs sampling, with applications to Bayesian inference. By the end of the course, students will be able to apply these tools to solve practical problems in statistical modeling and data analysis.

The Bruin Learn course page is here.

A detailed description of the class is available here.

Motivation and Synopsis

During the twentieth century, the development of statistical computing played a crucial facilitating role for the growth of the statistics discipline and the adoption of statistical methods within the scientific community and beyond. In the twenty-first century, the amounts of data available for statistical analysis has grown tremendously, yielding new opportunities for statistical computing, as well as new challenges. Statistical computing constitutes an important part of a statistics education, and is highly valuable for statisticians where ever they may work.

This course introduces Monte Carlo methods for simulation, optimization, estimation, learning and complex landscape visualization, including: Importance sampling; Sequential importance sampling; Markov chain Monte Carlo (MCMC) sampling techniques including Gibbs samplers, Metropolis/Hastings and various improvements; Simulated annealing; Convergence analysis; Data augmentation; If there is time I will introduce Hamiltonian and Langevin Monte Carlo.

The primary purpose of this course is to provide students with a common set of core knowledge about statistical computing for their class work and research. The course will have an applied focus on tools. The course will involve the practical application of the ideas of statistical computing and their implementation through statistical software, particularly R.

Prerequisites

• Statistics 100B (Introduction to Mathematical Statistics) or Mathematics 170S (Applied Statistics: Probability and Statistics for Engineers)
• Statistics 102A (Introduction to Computational Statistics with R)
• People who didn’t take 102B before may still take this class as long as they have background on matrix algebra, probability theory, and programming skills. To do this attend the first classes and we can assess if this is advisable.