This course is conceived as the sequel to the first introduction to mathematical statistics in Leiden, which is the basic material on statistical testing, estimation and confidence intervals usually taught from the book of J.A. Rice “Mathematical Statistics and Data Analysis”, chapters 7, 8, 9 and 10 (pub. Duxbury press), together with usually a quick introduction to regression analysis (chapter 14).
I plan to start by reviewing regression analysis and also looking at “analysis of variance”, chapter 12 from Rice. We will see that analysis of variance can also be cast in the form of the general linear model, studied in regression analysis; the rather special looking analysis methods described in Rice are nothing else than yet more applications of the least squares method; which itself is nothing else than maximum likelihood estimation under the assumption of normal errors.
After that I would like to treat some more advanced topics related to linear models. What they would be, would depend very much on the interests of the students. I see two main options
1) if there are many students who have a general and practical inclination I would like to steer the course in the direction of a variety of modern applied statistical methods for dealing with multivariate data, especially regression type models but no longer necessarily linear or even parametric. I would use the book “Modern Applied Statistics with S” by W.N. Venables and B.D. Ripley (pub. Springer), and the students will do some applied data analysis themselves.
By the way, the S language for statistical analysis has been implemented under the name “R”, and is freely available and widely used everywhere where experimental statistical methodology is developed. A huge user’s community has contributed many specialist packages to the system.
2) if there are many students of a more theoretical inclination we could study J.R. Rao‘s classic book “Linear Statistical Inference and its Applications” which goes much more deeply into the mathematics of the standard linear model.
In recent years the course followed the line of option 1) and an alternative title would be “Modern Applied Statistics with R”.
Mathematical Statistics and Data Analysis by J.A. Rice (2006: 3rd edition), Duxbury Press
Modern Applied Statistics with S by W.N. Venables and B.D. Ripley (2002: 4th edition) pub. Springer
First courses in probability and in statistics. It would be useful to have prior experience with LaTeX, and to have use during the course of your own laptop (First assignment: install R and LaTeX).
Three mini-projects (data analysis with R) to be carried out, written up and submitted during the course. (No written examination). Students may at the end of the course do one further project in order to earn 2 more EC’s .