Susu Zhang (szhan105 at illinois dot edu)
Statistical Computing involves the use of computer-intensive methods to address statistical problems, for example, drawing samples from analytically intractable distributions and approximating the sampling distribution of a statistic. These computational approaches are very useful for statistical inference and parameter estimation (both frequentist and Bayesian). Throughout this course, you will learn about the commonly used statistical computing methods, including
random variable generation;
Monte Carlo integration and inference;
resampling methods (e.g., bootstrap, permutation tests);
Markov Chain Monte Carlo methods;
numerical analysis tools (e.g., nonlinear equation-solving, optimization, and numerical integration); and
the Expectation-Maximization (EM) algorithm.
We will introduce why they work, how they work (with examples), and how to practically implement these algorithms in the R programming environment.
Week 1 (1/17 - 1/21): Random variable generation - Part I (Slides, R script)
Week 2 (1/22 - 1/29): Random variable generation - Part II (Slides, R script)
Week 3 (1/31 - 2/4): Monte Carlo Integration - Part I (Slides, R script)
Week 4 (2/5 - 2/11): Monte Carlo Integration - Part II (Slides, R script)
Week 5 (2/12 - 2/14) Monte Carlo Inference - Part I (Slides, R Script)
Week 6 (2/16 - 2/26) Monte Carlo Inference - Part II (Slides, R Script)
Week 7 (2/28 - 3/1) Resampling - Part I (Slides, R Script)
Week 8 (3/4 - 3/10) Resampling - Part II (Slides, R Script)
Week 9 (3/20 - 3/22) Resampling - Part III (Slides, R Script)
Week 10 (3/25 - 3/29) MCMC - Part I (Slides)
Week 11 (4/5 - 4/8) MCMC - Part II (Slides, R Script)
Week 12 (4/10 - 4/15) MCMC - Part III (Slides, R Script)
Week 13 (4/17 - 4/24) Nonlinear Optimization (Slides, R Script)
Week 14 (4/26 - 4/29) EM Algorithm (Slides, R Script)
These are the recordings from Spring 2021 when the course was taught asynchronously. Over time, some materials/examples have been updated, but these clips broken down into mini topics could be a helpful reference.