MAS2901 : Introduction to Statistical Inference
- Offered for Year: 2018/19
- Module Leader(s): Dr Kevin Wilson
- Owning School: Mathematics, Statistics and Physics
- Teaching Location: Newcastle City Campus
|Semester 1 Credit Value:||10|
To lay the foundations of statistical inference. The students will learn about the distinction between a population and a sample. They will know about the use of estimators calculated from random samples as a means of learning about properties of the population. They will be able to describe the role of likelihood methods in the derivation of estimators and their properties.
Statistics aims to learn about populations on the basis of samples drawn from them. Population parameters, such as means, can be estimated by suitable sample statistics, but they will be in error because of sample to sample variation. Statistical inference is concerned both with estimating parameters and also with quantifying the associated sampling variation.
This module introduces fundamental notions of a standard error, confidence interval and hypothesis tests, in the context of both discrete and continuous variables. The likelihood is probably the most important concept in statistical methodology, and its introduction in the case of a scalar parameter is one of the main features of the module.
Outline Of Syllabus
Notion of an estimator: examples using means and proportions.
Properties of sampling distributions, including standard errors and confidence intervals.
Simulation of a sampling distribution.
Central Limit Theorem via simulation, no proof.
Likelihood, maximum likelihood estimators (scalar case) and their properties, including the illustration of these using simulation. Likelihood ratio test. Sufficiency.
Introduction to hypothesis tests: rejection regions, type I and type II errors, power and significance level. Most powerful tests via the Neyman-Pearson Lemma. Illustrations using one- and two-sample hypothesis tests for means and for proportions.
|Scheduled Learning And Teaching Activities||Lecture||1||1:00||1:00||Class test|
|Scheduled Learning And Teaching Activities||Lecture||3||1:00||3:00||Problem classes|
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Lecture||25||1:00||25:00||Formal lectures|
|Guided Independent Study||Assessment preparation and completion||1||6:00||6:00||Revision for class test|
|Guided Independent Study||Assessment preparation and completion||1||13:00||13:00||Revision for unseen exam|
|Guided Independent Study||Assessment preparation and completion||1||2:00||2:00||Unseen exam|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||4||1:00||4:00||Tutorials in the lecture room|
|Guided Independent Study||Independent study||1||11:00||11:00||Studying, practising and gaining understanding of course material|
|Guided Independent Study||Independent study||1||12:00||12:00||Preparation for project|
|Guided Independent Study||Independent study||3||3:00||9:00||Review of coursework assignments, project and course test|
|Guided Independent Study||Independent study||2||6:00||12:00||Preparation for coursework assignments|
Teaching Rationale And Relationship
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.
The format of resits will be determined by the Board of Examiners
|Written Examination||40||1||M||5||Class test|
|Prob solv exercises||1||M||5||Coursework assignments|
|Prob solv exercises||1||M||5||Project|
Assessment Rationale And Relationship
A substantial formal unseen examination is appropriate for the assessment of the material in this module. The coursework assignments will consist of two written assignments of approximately equal weight. The coursework assignments, the project and the (in class, therefore 40 minute) coursework test allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these are thus formative as well as summative assessments.