Bulletin Description
Prerequisite: Graduate standing; upper-division standing with MATH 441 or equivalent; or permission of the instructor.
Exploration of efficient methods for obtaining numerical solutions to statistically formulated problems. Emphasis on basic R programming, random variable generation, bootstrap, Jackknife and its applications, methods for variance reduction, Monte Carlo simulation and integration, optimization techniques, Newton-Raphson algorithm, EM algorithm, Metropolis-Hasting algorithm, and Gibbs samplers.
Student Learning Outcomes
Upon completion of this course a student should be able to
- Learn how to simulate discrete and continuous random variables using inverse transform, general transformations and accept/reject methods.
- Obtain the hands-on experience on statistical analysis using bootstrapping and jackknife methods.
- Learn how to use variance reduction techniques.
- Master the skills to perform Monte Carlo simulations and integrations.
- Learn the principals and be able to use the optimization techniques: Newton Raphson and Expectation Maximization algorithms
- Obtain the hands-on experience on using Metropolis-Hastings and Gibbs Samplers algorithms.
Course Outline
- Introduction to R Programming (1 week)
- Review of probability theory and statistical inference (1 week)
- Generating of discrete random variables (1 week)
- Generating of continuous random variables (2 weeks)
- Bootstrap, Jackknife and some applications (1 week)
- Methods for Variance reduction (2 weeks)
- Monte Carlo Simulations and Integration (2 weeks)
- Optimization techniques: Newton-Raphson, Expectation-maximization (EM) algorithm (2 weeks)
- Metropolis-Hastings Algorithm (1 weeks)
- Gibbs Samplers (1 week)
Textbooks & Software
1. Statistical Computing with R by M. Rizzo, Chapman and Hall. Course notes/handouts.
2. Introducing Monte Carlo Methods with R, Robert, Christian P. and Casella, George (2010), Springer.
3. Simulation, by S. Ross, Elsevier.
R, by R Development Core Team