SATAISTICAL
COMPUTING
SPRING 2014
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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 406
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 every week. The course
grade will be based on about 14 homework assignments (65%), one midterm
exam (15%),
and one final exam (20%).
COURSE OUTLINE
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 |
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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, Linux |
LaTeX
documentation: http://latex-project.org/guides/ Linux
introduction (Chinese): |
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3 |
Random
number generation |
NAS Chapter 22 MASS Section 5.2 SCR Chapter 3 |
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4 |
Monte
Carlo methods in inference |
SCR 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 |
EM
algorithm |
NAS Chapter 13 SCR Section 11.7 |
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8 |
Optimization:
Newton-Raphson, Fisher scoring |
NAS Chapter 14 |
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9 |
Nonlinear
regression, iteratively reweighted least squares |
NAS Sections 14.6 and 14.7 |
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10 |
EM
algorithm extensions |
NAS Chapter 13 |
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11 |
Constrained
optimization |
NAS Chapters 11 and 16 SCR Section 11.8 |
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12 |
Numerical
integration |
NAS Chapter 18 SCR Section 11.3 |
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13 |
Markov
chain Monte Carlo I |
NAS Chapters 25 and 26 SCR Chapter 9 |
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14 |
Markov
chain Monte Carlo II |
NAS Chapters 25 and 26 SCR Chapter 9 |