統計計算

This course will introduce topics in numerical analysis useful for statistical modeling and analysis. Topics include computer programming, random number generation, Monte Carlo simulation, permutation test and the bootstrap, numerical linear algebra, the EM algorithm, optimization, nonlinear regression, numerical integration, and Markov chain Monte Carlo.

Students are expected to have background on undergraduate probability, and mathematical statistics. Computer programming knowledge on R/S-Plus/Matlab and/or C/C++ is required.

Class website: http://ghuang.stat.nctu.edu.tw/course/statcomp18/

There will be homework assignments almost every week. The course grade will be based on about 12 homework assignments (65%), one midterm exam (15%), and one final exam (20%).

• Introduction to statistical computing, R
• Introduction to LATEX, Linux
• Random number generation
• Monte Carlo methods in inference
• Bootstrap, jackknife and permutation tests
• Numerical linear algebra
• Optimization: Newton-Raphson, Fisher scoring
• Nonlinear regression, iteratively reweighted least squares
• EM algorithm
• Numerical integration
• Constrained optimization
• Markov chain Monte Carlo I
• Markov chain Monte Carlo II

Handouts corresponding to each lecture will be available on the class website before each class. Reading assignments are from the following three books: Lange K (2010). Numerical Analysis for Statisticians, 2nd edition. Springer. (NAS) Venables WN and Ripley BD (2002). Modern Applied Statistics with S, 4th edition. Springer. (MASS) Rizzo ML (2007). Statistical Computing with R. Chapman & Hall. (SCR)

地點

423 Joint Education Hall

時間

By appointment

聯絡方式

Phone: 03-513-1334 Email: ghuang@stat.nctu.edu.tw