BS2 Further Statistical Inference HT08

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.

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

Here you can download all overheads in a single file.

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 lovely 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

Last updated: Wednesday, 02 April 2008 11:32.  Steffen L. Lauritzen