University of Cambridge > Mathematics > Statistical Laboratory > David Spiegelhalter

Statistics IB

This is a home page for a course of 16 lectures to second year Cambridge mathematics students over 8 weeks.

The schedule

Estimation: Review of distribution and density functions, parametric families. Examples: binomial, Poisson, gamma. Sufficiency, minimal sufficiency, the Rao-Blackwell theorem. Maximum likelihood estimation. Confidence intervals. Use of prior distributions and Bayesian inference. [5]

Hypothesis testing: Simple examples of hypothesis testing, null and alternative hypothesis, critical region, size, power, type I and type II errors, Neyman-Pearson lemma. Significance level of outcome. Uniformly most powerful tests. Likelihood ratio, and use of generalised likelihood ratio to construct test statistics for composite hypotheses. Examples, including t-tests and F-tests. Relationship with confidence intervals. Goodness- of-fit tests and contingency tables. [4]

Linear models: Derivation and joint distribution of maximum likelihood estimators, least squares, Gauss-Markov theorem. Testing hypotheses, geometric interpretation. Examples, including simple linear regression and one-way analysis of variance. *Use of software*. [7]

Lectures

My board work is atrocious, and so all lecture notes will be pre-prepared and projected. They are placed here as 4-to-a-page pdfs, and you are encouraged to print them out for annotation during the lectures. I am very grateful to Susan Pitts for providing much of this material.

I include R code for examples in the notes, but this is non-examinable.

Further notes can be obtained from Richard Weber's page for this course. However note that the course schedule has changed since these notes were written in 2007, and the new schedule covers the general linear model, and Gauss-Markov theorem, which is not covered in Professor Weber's notes, which also include Computational Methods (Lecture 15) and Decision Theory (Lecture 16), which we will not be covering.

This material is provided for students, supervisors (and others) to freely use in connection with this course. Copyright remains with the author.

Examples sheet

There will be three examples sheets. Here is the first one. Here is the second one. Here is the third one.

Distributions and Statistical Tables

Details of probability distributions are available here.

Selected percentiles of t, Normal, chi-squared and F distributions are available here.

Interludes

I will include a short (non-examinable) interlude in each lecture to try and give an idea of how statistical ideas are used in contemporary society. These will be available on this site after the lecture.

Exam questions

Questions since 2001 can be found here.

Note the syllabus changed in 2008-9.

Recommended Books

  1. G. Casella and J. O. Berger, Statistical Inference, 2nd Edition, Brooks Cole, 2001, ISBN 0-534-24312-6.
  2. D. A. Berry and B. W. Lindgren, Statistics, Theory and Methods, Duxbury Press, 1995, ISBN 0-534-50479-5.
  3. M. H. De Groot, Probability and Statistics, 3rd edition, Addison-Wesley, 2001, ISBN 0-201-52488-0.

Other general resources

University of Cambridge > Mathematics > Statistical Laboratory > David Spiegelhalter

*Last modified: 10 March 2017** *