Course Coordinator: 
Kenji Doya
Statistical Methods

This course introduces basic principles and practical methods in statistical testing, inference, validation, and experimental design. The lectures cover the following topics: What is probability: frequentist and Bayesian views; probability distributions; Statistical measures; Statistical dependence and independence; Stochastic processes; Information theory; Statistical testing; Statistical inference: maximum likelihood estimate and Bayesian inference; Model validation and selection; Experimental design. Emphasis is put on the assumptions behind standard statistical methods and the mathematical basis for finding the right one.

This basic course will equip students with the necessary understanding and experience in statistical methods essential to modern scientific research.
Detailed Syllabus: 
  1. What is probability: frequentist and Bayesian views
  2. Statistical measures and Information theory
  3. Statistical dependence and independence
  4. Statistical testing
  5. Random numbers, random walks, and stochastic processes
  6. Regression and correlation analysis
  7. Analysis of variance I
  8. Analysis of variance II
  9. Statistical inference: maximum likelihood estimate and Bayesian inference
  10. Model validation and selection
  11. Experimental design
  12. Experimental design II
  13. Conditional probability
  14. Special probability densities and distributions
  15. Revision and conclusions
Course Type: 
Problem sets, 60%; Final written test, 40%.
Text Book: 
All of Statistics - A Concise Course in Statistical Inference, by Larry Wasserman (2003) Springer
All of Nonparametric Statistics, by Larry Wasserman (2005) Springer
Reference Book: 
Pattern Recognition, 4 edn, by S. Theodoridis and K. Koutroumbas (2008) Academic Press
Neural Networks for Pattern Recognition, by Christopher Bishop (1996) Oxford University Press