BS2 Further Statistical Inference HT09

Overview of Lectures

This course builds on BS2a: Foundations of Statistical Inference and aims to give an understanding of fundamental issues associated with model-based statistical inference in high-dimensional statistical problems in a frequentist and Bayesian perspective as well as in a sequential setting.

The content of each of the lectures is given below.

The overheads will appear on this website some time before the lecture is held, occasionally at the last minute. There is similar material available for the course held last year. Please note that the overheads may contain serious mistakes and misprints so you must work critically through them.

1. Ancillarity and conditional inference
2. Nuisance parameters and their treatment
3. More on nuisance parameters
4. Newton-Raphson iteration and the multivariate method of scoring.
5. Generalized linear models
6. The multivariate Gaussian distribution
7. Multivariate Gaussian models and the Wishart distribution
8. Wilks' distribution and Hotelling's T^2
9. Wishart and InverseWishart distribution
10. Laplace's method of integrals and Bayesian asymptotics
11. Bayesian model comparison
12. Alternative methods for model comparison
13. Saddle-point approximations and asymptotics of the MLE
14. Sequential Bayesian updating.
15. Kalman filter and smoother. Particle filters.
16. Kalman filter and smoother

Classes

Much of the material can be found in

G. A. Young and R. L. Smith, Essentials of Statistical Inference, Cambridge University Press, 2005.

T. Leonard and J. S. J. Hsu, Bayesian Methods, Cambridge University Press, 2005.

In addition I suggest the little book

S. D. Silvey, Statistical Inference, Chapman and Hall, 1975.

But it could be helpful also to read in

D. R. Cox, Principles of Statistical Inference, Cambridge University Press, 2006.

Further recommendations for reading will be given with the specific topics covered as we go along.

Course page

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Last updated: 08 April 2009. Steffen L. Lauritzen