NATIONAL CHIAO TUNG UNIVERSITY
INSTITUTE OF STATISTICS
SATAISTICAL COMPUTING
SPRING 2018
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Instructor: |
Guan-Hua Huang, Ph.D. |
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Office: 423 Joint Education Hall |
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Phone: 03-513-1334 |
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Email: ghuang@stat.nctu.edu.tw |
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Class meetings: |
Friday 13:20-16:20 at A203 Joint Education Hall |
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Office hours: |
By appointment |
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Class website: |
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Credit: |
Three (3) credits |
COURSE SUMMARY
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.
HANDOUTS AND TEXTBOOKS
Handouts corresponding to each lecture will be available on the class website before each class. Reading assignments are from the following three books:
Ÿ Lange K (2010). Numerical Analysis for Statisticians, 2nd edition. Springer.
Ÿ Venables WN and Ripley BD (2002). Modern Applied Statistics with S, 4th edition. Springer.
Ÿ Rizzo ML (2007). Statistical Computing with R. Chapman & Hall.
PREREQUISITES
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.
METHOD OF STUDENT EVALUATION
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%).
COURSE OUTLINE
Readings refer to:
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)
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Module |
Topic |
Reading |
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1 |
Introduction to statistical computing, R |
MASS Chapters 1-4 The R manuals: http://cran.r-project.org/manuals.html SCR Chapter 1 |
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2 |
Introduction to LATEX |
LaTeX documentation: |
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3 |
Random number generation |
NAS Chapter 22 SCR Chapter 3 MASS Section 5.2 |
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4 |
Monte Carlo methods in inference |
SCR Section 5.2, and Chapter 6 |
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5 |
Bootstrap, jackknife and permutation tests |
NAS Chapter 24 SCR Chapters 7 and 8 |
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6 |
Numerical linear algebra |
NAS Chapters 7, 8 and 9 |
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7 |
Optimization: Newton-Raphson, Fisher scoring |
NAS Chapter 14 SCR Sections 11.4, 11.5 and 11.6 |
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8 |
Nonlinear regression, iteratively reweighted least squares |
NAS Sections 14.6 and 14.7 |
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9 |
EM algorithm |
NAS Chapter 13 SCR Section 11.7 |
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10 |
Numerical integration |
NAS Chapter 18 SCR Section 11.3 |
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11 |
Constrained optimization |
NAS Chapters 11 and 16 SCR Section 11.8 |
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12 |
Markov chain Monte Carlo I |
NAS Chapters 25 and 26 SCR Chapter 9 |
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13 |
Markov chain Monte Carlo II |
NAS Chapters 25 and 26 SCR Chapter 9 |