Mathematical Statistics

Course Coordinator: Dr Tony M T Chan, Grad Dip, MPhil (CUHK), PhD (CityU)

Course Developer: The Open University, UK, Course Team

STAT S347 is a higher-level course in statistics and mathematics and is an elective in the Statistics and Decision Science, and Mathematical Studies programmes. The course introduces the mathematical theory underlying the methods and techniques used in applications of statistical analyses and inference. The course covers four areas. It first reviews the applied probability and distribution theory. The second part focuses on statistical inference such as maximum likelihood estimation, point estimation and hypothesis testing. The third part covers Bayesian statistics which includes the Markov chain Monte Carlo technique. The final part examines the statistical modelling including regressions models and generalized linear models using the Bayesian approach. STAT S347 contains integrated multimedia components throughout the study units.

Advisory pre-requisites
Student taking this course will need a sound knowledge of basic statistics and be reasonably competent in calculus, algebra and matrices. They are advised to have already studied one of the following mathematics courses: MATH S121 or MATH S221, and one of the following statistics courses: STAT S242 or MATH S280, or equivalent before studying this course.

Aims
This course aims to:

• provide an advanced understanding of the principles of probability, standard univariate and multivariate continuous distributions and their applications in a variety of real-world problems.

• develop a solid understanding of decision theory, point estimation, confidence intervals, and hypothesis testing.

• equip students with a theoretical foundation in the methods of statistical inference with practical applications in data analysis.

• provide practical training in Bayesian statistics and its applications in science, business, economic and financial mathematics.

• develop knowledge and understanding of the use of the Bayesian approach to modelling the regression and the generalized linear models.

Contents
The course covers the following topics:

Block 1: Review of distribution theory

• Reviewing the relevant elements of statistical concepts and probability theory
• Univariate and multivariate continuous distribution theory

Block 2: Classical statistical inference

• Maximum likelihood estimation, likelihood ratio tests
• The theory of estimation, significance testing and confidence intervals

Block 3: Bayesian statistics

• Bayesian inference as a decision problem
• The Markov chain Monte Carlo technique

Block 4: Linear modelling

• The theory of linear and multiple regression statistical models.
• The Bayesian approach to modelling the general and the generalized linear models.

Learning support
There are regular two-hour lectures and surgeries throughout the presentation of the course.

Assessment
There are four assignments, from which the best three scores count towards the final grade, and a final examination. Students are required to submit assignments via the Online Learning Environment (OLE).

Online requirement
Through the OLE, you can communicate electronically with your tutor and the Course Coordinator as well as other students. To access the OLE, you will need to have Internet access. The use of the OLE is required for the study and assessment of this course.

Set book(s)
There will be no set book for this course.

Students with disabilities or special educational needs
Students with impaired vision may have difficulties but other students with disabilities or special educational needs should be able to cope with the essential parts of the course. When in doubt, advice should be sought from the Course Coordinator.