Matrices in Statistics with Applications 2020
The purpose of the course is to give the participants an introduction to numerical techniques that are of importance in
statistics and a flavour of handling large scale problems in Computational Statistics.
The course is intended for students and researchers in various fields where Statistics is used as a modelling and analysis tool.
Basic knowledge in linear algebra and scientific computing; basic knowledge of stochastic variables, statistical distributions.
General aims of the course
The aim of the course is to enable students to understand and use important techniques in Computational Statistics. The students will study computational methods used in Statistics with emphasis on large-scale computations and will develop understanding and skills how to use these appropriately in research and applications.
These insights should be applied in practice in solving problems of relevance of the participant’s PhD-project.
The course discusses selected topics in Computational Statistics, and promotes the understanding of the crucial role of numerical computation in modern statistical research and application of statistical methods to real-life problems. The focus is on solving computationally intensive tasks, enabled by the availability of powerful computer facilities.
The course includes theory and methods of numerical linear algebra, suited for statistical computing, linear regression models, data mining, pattern recognition, principal component analysis, singular value decomposition, Markov Chain Monte Carlo methods, networks, graphs, and matrices, sparse matrices.
Course schedule (detailed schedule)
The course consists of:
- 1 week pre-study exercises 7-11 September.
- 1 week of lectures and hands-on Uppsala , 14-18 September.
- 1 week project assignment 21-25 September.
Review material for self study:
In order to follow the course material, the following basic concepts and definitions from Statistics and Linear Algebra have to be reviewed.
- Linear systems, singular/non-singular matrix, (column/row) rank , tridiagonal (band) matrix, LU, and Gaussian elimination. Read: (Wikipedia source NLA) or some other introductor text.
- Basic knowledge of stochastic variables, statistical distributions. Read (Wikipedia source Stat) or some other introductor text.
James E. Gentle, Computational Statistics, Springer, 2009.
Lars Eldén. Matrix methods in data mining and pattern recognition, 2nd ed, SIAM, Philadelphia, 2019.
Lars Eldén, Linde Wittmeyer-Koch, Hans Bruun-Nielsen, Intrduction to numerical computations, Studentlitteratur, 2001. Freely available here.
Peter Dalgaard, Introductory Statistics with R, Springer, 2002.
W.John Braun, Duncan J. Murdoch, A First Course in Statistical Programmimg with R, Cambridge University Press, 2007.
Geof H. Givens and Jennifer A. Hoeting, Computational Statistics, Wiley, 2005.
Wendy L. Martinez and Angel R. Martinez, Computational Statistics Handbook with MATLAB, Chapman & Hall/CRC, 2002.
Maya Neytcheva, Department of Information Technology, Uppsala University