This course is organized by the NGSSC Graduate School.

It consists of two parts, the first of which will be given at the Department of Mathematics, University of Linköping, and the second part will be given at the Department Information Technology, Uppsala University.

As a part of the work to be done within the course, a self-study part is included, to take place during Week 38 (September 15-19) 2008.

Review material for Week 38's self study:

• Linear systems, rank, singular matrix, non-singular matrix, tridiagonal (band) matrix, LU, and Gaussian elimination.
  Read:
  • Eldén, Wittmeyer-Koch, Bruun-Nielsen, Introduction to numerical computations, Studentlitteratur, 2001, (here)
  • (Wikipedia source) or some other introductor text.
• Basic knowledge of stochastic variables, statistical distributions. Read
  • (Wikipedia source)
  • or some other introductor text.
• Those who want to learn R well and use it in the course, should carefully study one of the two suggested books ([1] or [2])

Detailed time schedule

Week	Date	Topic(s)	Time	Location
39	Sep 22	Introduction. General description of the course. Computational Statistics - the statistician's point of view and the numerical analyst's point of view	9:15-12:00	????
		The statistical language R - short introduction. Computer lab exercises	13:15-17:00	????
	Sep 23	Regression problems with sparse data matrices. Sparse matrices - storage formats. Solving least squares problems with sparse matrices: direct and iterative methods. Computing the SVD	9:15-12:00	????
		Computer lab: Handling sparse matrices in R and MATLAB. Regression. Text mining	13:15-17:00	????
	Sep 24	Regression analysis (cont). Rank deficiency. Singular value decomposition (SVD). Pseudo-inverses. Shrinkage methods. Cross validation	9:15-12:00	????
		Computer lab: Numerical rank deficiency, collinearity. Application in pattern recognition: classification of handwritten digits (regression)	13:15-17:00	????
	Sep 25	Regression problems with sparse data matrices. Sparse matrices - storage formats. Solving least squares problems with sparse matrices: direct and iterative methods. Computing the SVD	9:15-12:00	????
		Computer lab: Handling sparse matrices in R and MATLAB. Regression. Text mining	13:15-17:00	????
	Sep 26	Concepts of numerical stability. Floating point computations - short introduction, variance example	9:15-12:00	????
		Computer lab: Floating point arithmetic - examples of loss of accuracy. Page ranking, the Google matrix	13:15-17:00	????
40	Sep 20-Oct 3	Work on Assignment (Part I) (download here)
41	Oct 6	Structured matrices in statistical applications. Structured covariance matrices - Toeplitz and circulant matrices. Invariant and shift-invariant systems. Fourier matrices	9:15-12:00	????
		Computer lab: Data simulations (generating test data with a required structure)	13:15-17:00	????
	Oct 7	Total Least squares (TLS): statistical view and numerical view. The issue of robustness	9:15-12:00	????
		Computer lab: Application of the TLS method	13:15-17:00	????
	Oct 8	Principal Component Analysis. Eigenvalue computations (large scale, sparse, loss of orthogonality). Partial Least Squares	9:15-12:00	????
		Computer lab: Eigenvalue computations, applications	13:15-17:00	????
	Oct 9	Random number generators. Markov chain Monte Carlo methods (MCMC). Parallelization issues, accuracy of the obtained solution	9:15-12:00	????
		Computer lab: MCMC application	13:15-17:00	????
	Oct 10	Discussion of the experiences from the last Computer lab}&9:00-9:30\\ &Overview of software tools for statistical computations (SPSS, SAS, R, MATLAB, Statistica, symbolic computations)	9:15-12:00	????
		Summary of the course material and sketch of new problems, methodologies, methods to be considered further	13:15-17:00	????
42	Oct 13 - 17	Work on Assignment (Part II) (not yet available)

Recommended books

1. Peter Dalgaard, Introductory Statistics with R, Springer, 2002.
2. W.John Braun, Duncan J. Murdoch, A First Course in Statistical Programmimg with R, Cambridge University Press, 2007.
3. Geof H. Givens and Jennifer A. Hoeting, Computational Statistics, Wiley, 2005.
4. Wendy L. Martinez and Angel R. Martinez, Computational Statistics Handbook with MATLAB, Chapman & Hall/CRC, 2002.
5. Lars Eldén. Matrix Methods in Data Mining and Pattern Recognition. SIAM, Philadelphia, PA, Philadelphia, PA, USA, 2007.

Organization issues:
Some instructions how to find us in Linköping are to be added.
Some instructions how to find us in Uppsala are to be found here .
Suggested hotel to book rooms in Linköping: Linköpings Vandrarhem & Hotell and Mjellerumsgården
Suggested hotel to book rooms in Uppsala: Hotel Uppsala .

For NGSSC students only:
Your home department is expected to provide advance payment for travel and housing. After the course has been completed, the costs will be reimbursed from NGSSC by a lump grant of SEK 12 000.