Dr Wicher Bergsma COL 6.06

This course is available on the MSc in Econometrics and Mathematical Economics, MSc in Statistics, MSc in Statistics (Financial Statistics), MSc in Statistics (Financial Statistics) (Research) and MSc in Statistics (Research). This course is available as an outside option to students on other programmes where regulations permit.

Students must have statistical knowledge up to the level of the course ST425: Statistical Inference: Principles, Methods and Computation. It is also useful to take ST411: Regression, Diagnostics and Generalised Linear Modelling in parallel to this course.

Our aim is to teach students important statistical methodologies that reflect the exciting development of the subject over the last twenty years, which include empirical likelihood, MCMC, bootstrap, local likelihood and local fitting, model Assessment and selection methods, and Gaussian process regression. These are computationally intensive techniques that are particularly powerful in analysing large-scale data sets with complex structure. A selection from the following topics will be covered: robustness of likelihood approaches: distance between working model and "truth", maximum likelihood under wrong models, quasi-MLE, model selection with AIC, robust estimation. Empirical likelihood: empirical likelihood of mean. Bayesian methods and Markov chain Monte Carlo (MCMC) basic Bayes, Gibbs sampler, Metropolis-Hastings algorithm. Elements of statistical learning: global fitting versus local fitting, linear methods for regression, splines, kernel methods and local likelihood. Model assessment and selection: bias-variance trade-off, effective number of parameters, BIC, cross-validation. Further topics: statistical learning using Gaussian process regression. The course will be continuously updated to reflect important new developments in statistics.

20 hours of lectures and 10 hours of seminars in the LT.

Week 6 will be used as a reading week.

Formative assessment consists of weekly exercises.

T Hastie, R Tibshirani & J Friedman, The Elements of Statistical Learning: Data Mining, Inference and Prediction;

Y Pawitan, In All Likelihood: Statistical Modelling and Inference Using Likelihood;

M A Tanner, Tools for Statistical Inference.

Exam (100%, duration: 2 hours) in the main exam period.