This course will focus on two important components of statistical computing: Monte Carlo integration strategies and optimization methods. We will survey a variety of techniques, ranging from classic to state-of-the-art. The course will be based on the book Computational Statistics, by Givens and Hoeting (Wiley), which covers these and other topics in greater detail. The course will include some examples from R software. Students should bring a laptop and have familiarized themselves with basic R commands and R programming before taking the course. The course will be starting at 8:30 in the morning of July 18th and last two days.
Many problems in statistics require the evaluation of integrals that cannot be solved analytically, particularly in Bayesian statistics. In the Monte Carlo integration section of the course, we will cover Monte Carlo integration, importance sampling and variance reduction techniques, and Markov chain Monte Carlo methods.
Optimization also plays a central role in statistics, particularly in numerical maximum likelihood estimation. In the optimization portion of the course, we will cover Newton-like methods, Gauss-Seidel iteration, tabu algorithms, simulated annealing, genetic algorithms, the EM algorithm and its variants.
We seek to give students a practical understanding of how and why existing methods work, enabling students to use modern statistical methods effectively. Examples are drawn from diverse fields including bioinformatics, ecology, and medicine. The course will include some examples from R software. Students should bring a laptop and have familiarized themselves with basic R commands and R programming before taking the course.