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.

無備註

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

  MASS: Chapters 1-4, The R manuals: http://cran.r-project.org/manuals.html, SCR: Chapter 1

• Introduction to LATEX, Linux

  LaTeX documentation: http://latex-project.org/guides/, Linux introduction (Chinese): http://linux.vbird.org/

• Random number generation

  NAS: Chapter 22, MASS: Section 5.2, SCR: Chapter 3

• Monte Carlo methods in inference

  SCR: Section 5.2, Chapter 6

• Bootstrap, jackknife and permutation tests

  NAS: Chapter 24, SCR: Chapters 7 and 8

• Numerical linear algebra

  NAS: Chapters 7, 8 and 9

• Optimization: Newton-Raphson, Fisher scoring

  NAS: Chapter 14 SCR: Sections 11.4, 11.5 and 11.6

• Nonlinear regression, iteratively reweighted least squares

  NAS: Sections 14.6 and 14.7

• EM algorithm

  NAS: Chapter 13, SCR: Section 11.7

• Numerical integration

  NAS: Chapter 18, SCR: Section 11.3

• Constrained optimization

  NAS: Chapters 11 and 16, SCR: Section 11.8

• Markov chain Monte Carlo I

  NAS: Chapters 25 and 26, SCR: Chapter 9

• Markov chain Monte Carlo II

  NAS: Chapters 25 and 26, SCR: Chapter 9

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