This course is organized by the NGSSC Graduate School.

It consists of two parts, which both 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 35 (August 29 - September 2) 2011.

Review material for Week 35'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])

Course materials (to be updated)

• Lars Eldén:
• Dietrich von Rosen:
• Maya Neytcheva: Slides and Labs

Detailed time schedule

Week	Date	Topic(s)	Time	Location	Lecturer
36	Sep 05	Introduction. General description of the course	9:15-9:30	1412	MN
		Computational Statistics - the statistician's point of view	9:30-11:00	1412	DvR
		Computational Statistics - the numerical analyst's point of view	11:15-12:00	1412	LE
		The statistical language R and Matlab - short introduction	13:15-15:30	1412	MN
		The statistical language R and Matlab - computer lab exercises	15:30-17:00	1412	MN
	Sep 06	Discussion of the experience from the last computer lab	9:15-9:30	1412	MN
		Regression analysis, statistical concepts	9:30-10:30	1412	DvR
		Least Squares and QR factorization	10:45-12:00	1412	LE
		Multiple regression. Normal equations vs QR factorization. Polynomial regression.	13:00-17:00	1412	LE
	Sep 07	Discussion of the experience from the last computer lab	9:00-9:30	1412	LE
		Regression analysis (cont). Rank deficiency. Singular value decomposition (SVD). Pseudo-inverses. Shrinkage methods. (Cross validation)	9:30-12:00	1412	LE
		Numerical rank deficiency, collinearity. Application in pattern recognition: classification of handwritten digits (regression)	13:15-17:00	1412	LE
	Sep 08	Discussion of the experience from the last computer lab	9:15-9:30	1412	LE
		Floating point computations - short introduction, variance example Graphs and their usage in Statistical applications (page-rank), regression trees and classification trees. Concepts of numerical stability	9:30-12:00	1412	LE
		Floating point arithmetic - examples of loss of accuracy. Page ranking, the Google matrix	13:15-17:00	1412	LE
	Sep 09	Discussion of the experience from the last computer lab	9:15-9:30	1412	MN
		Regression problems leading to sparse matrices	9:30-12:00	1412	DvR
		Sparse matrices - storage formats. Solving least squares problems with sparse matrices: direct and iterative methods. Computing the SVD	10:45-12:00	1412	MN
		Handling sparse matrices in R and MATLAB. Regression. Some parallelization issues, related to data structure	13:15-17:00	1412	MN
37	Sep 12-Oct 16	Finalize and send all lab reports from the first course week.
38	Sep 19	Partial Least Squares	9:15-12:00	1412	LE
		Partial Least Squares	13:15-17:00	1412	LE
	Sep 20	Discussion of the experience from the last computer lab	9:15-9:30	1412	MN
		Principal Componennt Analysis and regression	9:30-10:30	1412	DvR
		Krylov subspace methods. Eigenvalue computations (large scale, sparse)	10:45-12:00	1412	MN
		Testing some classical computational methods	13:15-17:00	1412	MN
	Sep 21	Discussion of the experience from the last computer lab	9:15-9:30	1412	MN
		Random number generators	9:30-10:15	1412	MN
		Markov chain Monte Carlo methods (MCMC)	10:30-12:00	1412	DvR
		MCMC	13:15-17:00	1412	DvR
	Sep 22	Discussion of the experience from the last computer lab	9:15-9:30	1412	DvR MN
		Parallel computing. Parallel Statistical computing	9:30-12:00	1412	MN
		Parallel programming in R and Matlab, examples	13:15-17:00	1412	MN
	Sep 23	Discussion of the experience from the last computer lab	9:15-9:30	1412	MN
		Summary of the course material and sketch of new problems, methodologies, methods to be considered further.	9:30-12:00	1412	LE DvR MN

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 Uppsala are to be found here .
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.