MAS2901 : Introduction to Statistical Inference

Semester 1 Credit Value: 10
ECTS Credits: 5.0


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.

Module summary

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.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Scheduled Learning And Teaching ActivitiesLecture11:001:00Class test
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture221:0022:00Formal lectures
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Scheduled Learning And Teaching ActivitiesDrop-in/surgery120:102:00Office hours
Scheduled Learning And Teaching ActivitiesDrop-in/surgery51:005:00Tutorials in the lecture room
Scheduled Learning And Teaching ActivitiesDrop-in/surgery120:102:00Office hours
Guided Independent StudyIndependent study17:007:00Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study112:0012:00Preparation for project
Guided Independent StudyIndependent study33:009:00Review of coursework assignments, project and course test
Guided Independent StudyIndependent study26:0012:00Preparation 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: a typical student might spend a total of one or two hours over the course of the module, either individually or as part of a group.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Description Length Semester When Set Percentage Comment
Written Examination1201A85N/A
Written Examination401M5Class test
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M5Coursework assignments
Prob solv exercises1M5Project
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 assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists