STAT 740: Statistical Computing, Fall 2017
Instructor: Tim Hanson. E-mail: hansont@stat.sc.edu.
Office Hours: Tuesday/Thursday 10am to 11am, and by appointment.
Office: 219C LeConte College, (803) 777-3859.
Class Meeting: 8:30am-9:45am Tuesday/Thursday, LeConte College 201A.
Textbook: Monte Carlo Statistical Methods, Second Edition by Christian P. Robert and George Casella.
Strongly recommended: Computational Statistics, Second Edition by Geof H. Givens and Jennifer A. Hoeting.
Prerequisites: STAT 713 or consent of instructor.
Course description
We will cover a good portion of Monte Carlo Statistical Methods, omitting some topics and introducing others. The primary computing language for the course is R, but you are encouraged to learn a compiled language on your own such as C++ or FORTRAN for your dissertation work. Topics include:
► Introduction: statistical models; likelihoods; deterministic vs. stochastic approaches; Newton-Raphson, asymptotic normality of MLE & multivariate delta method.
► Bayesian approach & simulation; random variable generation: inverse CDF; transformations; accept-reject; envelope methods; simulating multivariate distributions; the method of composition & sampling mixtures.
► Integration: classical Monte Carlo; importance sampling; trapezoidal & simpsons rule; Gaussian quadrature & Laplace approximations.
► Optimization: iterative procedures revisited; expectation-maximizaton (EM); stochastic EM; simulated annealing.
► Markov chain Monte Carlo (MCMC) for Bayesian inference: Gibbs sampling; Metropolis-Hastings (M-H); adaptive M-H; slice sampling; convergence diagnostics & posterior inference; estimation of posterior quantiles & HPD intervals; use of JAGS software in R & PROC MCMC in SAS.
► Model selection: various criteria including cross-validation, AIC, BIC, DIC, WIC, LPML; Bayes factors and the Savage-Dickey ratio; reversible jump MCMC.
► Resampling methods: parametric and nonparametric bootstrap.
► If time permits, Smoothing: kernel density estimation; splines; and LOESS.
Learning outcomes
Learning Outcomes. By the end of the course students should be able to:
► understand algorithms for numerical integration and optimization apply them to obtain inference from statistical models;
► hand-program and validate various algorithms in R to obtain inference from a variety of models;
► be aware of canned programs and R packages that allow the automated fitting of some models;
► have a working knowledge of various model selection techniques; and
► have basic knowledge of some approaches to nonparametric smoothing and resampling methods.
Computing
Algorithms will be broadly illustrated using R. You are encouraged to learn and use a compiled language such as C++ or FORTRAN for your dissertation work on your own.
Accommodations for disabilities
If you require special accommodations for a disability, these must be arranged in advance through the Office of Student Disability Services in room 112A LeConte (777-6142, TDD 777-6744, sasds@mailbox.sc.edu).
Homework
Homework will consist of implementing and testing various algorithms in R. Some minor "paper and pen" theoretical derivations may be asked for too. The last homework may be a more involved course project depending on how the semester proceeds.
Grading
The minimum percent needed for each grade is: A 90% B+ 87% B 80% C+ 77% C 70% D 60%. Those with a final course percentage under 60% receive an F.
Honor Code
The official honor code is the Carolinian Creed in the Carolina Community: Student Handbook & Policy Guide. If you violate the honor code, I am required to report the case to the University's academic integrity office. If you are "found responsible" in the ensuing deliberations, the penalty will be at least a letter grade in the course. Examples of honor code violations include but are not limited to: copying, or allowing someone else to copy, solutions to assignments; posing as another student to do assignments or exams; hiring or persuading someone else to do assignments in your place, etc.