Course Details in

Module Title	Statistical Inference
School	Mathematics
Department	Mathematics
Module Code	06 22433
Module Lead	Dr DFM Hermans
Level	Honours Level
Credits	20
Semester	Full Term
Pre-requisites	Analytical Techniques - (06 22488) Statistics II - (06 22506)
Co-requisites
Restrictions	Pre-requisites 06 22488 and 06 22506. This module cannot be combined with the following: 06 22434 LM Statistical Inference
Contact Hours	Lecture-46 hours Tutorial-10 hours Total: 56 hours
Exclusions
Description	This module will give a comprehensive foundation to parametric likelihood based methods, which lie at the heart of modern statistical inference, the theoretical underpinning of an enormeous variety of practically useful statistical methodologies. The first part of this module will develop the ideas of maximum likelihood estimation first introduced in MSM202 (0613555/6). A variety of statistical models, Normal, binomial, Poisson, Weibull, will be used to illustrate the new theory. This module will also give an introduction of exponential family of distributions to unify many well-known standard probability models with regards to inference. In the second part of the module a major topic of discussion will be large sample theory. The basic concept of probability convergence will be explained and used to study 'convergence' of estimator, concept of convergence in distribution and CLT will be discussed to help obtain asymptotic distributions of estimators and test statistics. Finally, Bayesian inferences will be introduced and will be illustrated through standard probability models.
Learning Outcomes	By the end of the module, the students should be able to: Understand and develop likelihood-based inference techniques - point and interval estimation, tests of hypothesis - and their applications to various distributions; Understand exponential family of distributions. In addition, students will have general understanding of large sample theory, that is, being able to approximate the probability distributions of an estimator or a test statsitics when the sample size is large. Students should have general understanding of Bayesian inference.
Assessment	22433-01 : CA Sem 1 : Coursework (10%) 22433-02 : CA Sem 2 : Coursework (10%) 22433-03 : Exam : Exam (Centrally Timetabled) - Written Unseen (80%)
Assessment Methods & Exceptions	90% based on a 3 hour written examination in the Summer Term; 10% based on work during term-time.
Other	None
Reading List