Frequentist Statistical Inference (Distance Learning)
| Code | School | Level | Credits | Semesters |
| MATH4078 | Mathematical Sciences | 4 | 20 | Autumn UK |
- Code
- MATH4078
- School
- Mathematical Sciences
- Level
- 4
- Credits
- 20
- Semesters
- Autumn UK
Summary
This module is concerned with frequentist (classical/frequentist) statistical inference, both its theory and its applications and builds on the fundamental ideas of statistics introduced in the module “Foundations of Statistics”. Topics such as maximum likelihood estimation, properties of estimators, confidence intervals, likelihood ratio tests are explored and the Delta Method is also presented. There is emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma. This module will also explore how computers can be utilised to perform statistical inference for non-standard (i.e. analytically intractable) problems by applying innovative statistical and numerical methods. Optimisation methods, the bootstrap algorithm and simulation techniques including Monte Carlo methods will be introduced in relation to problems of statistical inference. Students will gain experience of linking the underlying statistical concepts to practical applications of the methodology. Students will gain experience of using statistical software and interpreting its output.
Target Students
Available to MSc Statistics Science (Distance Learning) students.
Classes
- Two 1-hour tutorials each week for 5 weeks
- Two 1-hour computings each week for 5 weeks
This module is designed for distance learning programmes where delivery of material will largely be asynchronous through course notes support by lecture videos, Moodle quizzes and exercises. The tutorial will be used to support and reinforce the asynchronous learning. The computer software learning will be through specially designed workbooks with support sessions through online computer labs.
Assessment
- 50% Coursework 1: To analyse a data set using statistical inferential and computational methods and interpret the analysis (20 pages)
- 50% Exam 1 (2-hour): Exam to assess statistical knowledge and understanding including aspects of computational methods.
Assessed by end of autumn semester
Educational Aims
The purpose of this course is to develop students’ knowledge and experience of the theory of frequentist statistical inference and their appreciation of how to implement the theory to real-life examples. The course will develop the statistical inference theory alongside the computational methods which are often required to implement the theory to real world problems.Learning Outcomes
A student who completes this course successfully will be able to:
L1 - state, derive and apply results underlying frequentist inference;
L2 - perform calculations for, and investigate optimality properties of, methods used in point and interval estimation and in hypothesis testing;
L3 - apply the delta method in univariate and multivariate settings;
L4 - state and use standard results relating to the theory and methods of the topics in computational statistics;
L5 - apply the theory and methods to a range of examples;
L6 - implement relevant computational methods using a statistical software package for performing statistical inference.
L7 - explain and interpret statistical results in the context of computational statistical inference.