Oliver Feng

This course is compulsory on the BSc in Actuarial Science, BSc in Actuarial Science (with a Placement Year) and BSc in Financial Mathematics and Statistics. This course is available on the BSc in Data Science, BSc in Econometrics and Mathematical Economics, BSc in Economics and Data Science, BSc in Mathematics and Economics, BSc in Mathematics with Data Science, BSc in Mathematics with Economics, BSc in Mathematics, Statistics and Business, Erasmus Reciprocal Programme of Study and Exchange Programme for Students from University of California, Berkeley. This course is freely available as an outside option to students on other programmes where regulations permit. It does not require permission. This course is available with permission to General Course students.

Pre-requisites:

Students must have completed ST206 before taking this course.

Additional requisites:

Students who have not taken ST206 should contact Dr Feng. Equivalent combinations may be accepted at the lecturer's discretion.

The course builds on the principles of probability and distribution theory covered in ST206 and introduces the statistical inference concepts needed for advanced courses in statistics and econometrics. The exact compositions of topics may vary from year to year, driven by the latest developments in statistical inference. The following are topics intended to be covered:

Random samples. Sample mean. Order statistics. Sample statistics. Sampling distributions. Parameter estimation. Sufficiency and minimal sufficiency. Maximum likelihood estimation. Rao–Blackwell theorem. Cramér–Rao lower bound. Interval estimation. Hypothesis testing. Likelihood ratio tests. Most powerful tests. Neyman–Pearson lemma. Linear regression. Least squares estimation. Generalised linear models. Bayesian inference.

20 hours of lectures, 10 hours of help session and 10 hours of seminars in the Winter Term.

Students will be expected to attempt 9 weekly homework assignments, which will be returned with feedback. If there is sufficient student demand, there will be the option of an exam-style class test in the Winter Term.

M C Mavrakakis & J Penzer, Probability and Statistical Inference: From Basic Principles to Advanced Models (primary reading)
G C Casella & R L Berger, Statistical Inference

Exam (100%), duration: 120 Minutes in the Spring exam period.