STATS 202C: Monte Carlo Methods for Optimization

2021-01-03

This course is a survey of Monte Carlo methods and numerical integration. Importance and rejection sampling. Sequential importance sampling. Markov chain Monte Carlo (MCMC) sampling techniques, with emphasis on Gibbs samplers and Metropolis/Hastings. Simulated annealing. Exact sampling with coupling from past. Permutation testing and bootstrap confidence intervals.

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 digital age, 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 in both academia and industry.

This graduate level 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; Exact sampling techniques; Convergence analysis; Data augmentation; Cluster sampling, such as Swendsen-Wang and SW-cuts; Hamiltonian and Langevin Monte Carlo; Equi-energy and multi-domain sampler; and Techniques for mapping complex energy landscapes

The primary purpose of this course is to provide students with a common set of core knowledge about statistical computing 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

  • Stat 202B: Matrix Algebra and Optimization.
  • People who didn’t take 202B 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.
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