Classical and Bayesian Inference
| Code | School | Level | Credits | Semesters |
| MATH4075 | Mathematical Sciences | 4 | 20 | Autumn UK |
- Code
- MATH4075
- School
- Mathematical Sciences
- Level
- 4
- Credits
- 20
- Semesters
- Autumn UK
Summary
This course is concerned with the two main theories of statistical inference, namely classical (frequentist) inference and Bayesian inference.
The classical inference component of the module builds on the ideas of mathematical statistics introduced in MATH4065.
Topics such as sufficiency, estimating equations, likelihood ratio tests and best-unbiased estimators are explored in detail.
There is special emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.
In Bayesian inference, there are three basic ingredients: a prior distribution, a likelihood and a posterior distribution, which are linked by Bayes' theorem.
Inference is based on the posterior distribution, and topics including conjugacy, vague prior knowledge, marginal and predictive inference, normal inverse gamma inference, and categorical data are pursued.
Common concepts, such as likelihood and sufficiency, are used to link and contrast the two approaches to inference.
Students will gain experience of the theory and concepts underlying much contemporary research in statistical inference and methodology.
Students will gain experience of using statistical software and interpreting its output.
A project will be undertaken which will involve analysing data using a statistical package and writing a short report.
Target Students
Only open to MSc students. All other students with suitable prerequisites should take the Level 3 (MATH3013) version instead.
Classes
- Two 1-hour lectures each week for 11 weeks
- One 1-hour computing each week for 3 weeks
Assessment
- 10% Coursework 1: Individual investigation using a computer package
- 90% Exam 1 (3-hour): Written examination.
Assessed by end of autumn semester
Educational Aims
The purpose of this course is to increase the students' knowledge and experience of the theory of statistical inference by studying in depth the classical and Bayesian approaches. Students taking it will acquire knowledge and skills relevant to a professional statistician.Learning Outcomes
A student who completes this course successfully will be able to:
L1 - State, derive and apply results underlying both (i) frequentist and (ii) Bayesian inference;
L2 - Perform calculations for, and investigate optimality properties of, methods used in point estimation and in hypothesis testing;
L3 - Apply the delta method in univariate and multivariate problems in both frequentist and Bayesian inference;
L4 - Perform standard Bayesian calculations in various single-parameter and simple multi-parameter problems;
L5 - Compare and contrast the frequentist and Bayesian approaches to inference;
L6 - Use of statistical software to perform analyses concerned with statistical inference;
L7 - Develop computing skills to perform statistical inference;
L8 - Write a short report based on the analysis of a dataset.