Undergraduate

modules

Modules

MAS2902 : Stochastic Modelling

Semesters
Semester 2 Credit Value: 10
ECTS Credits: 5.0

Aims

This module will provide an introduction to ways of mathematically describing processes that exhibit variability. Students will learn about the use of linear models to build statistical descriptions of data and about the use of simple probability distributions to provide useful models for many applications. Students will be able to use regression analysis in some simple cases; they will be able to apply Poisson Processes to model relevant random processes

Module summary

The module will introduce students to two distinct areas of stochastic modelling. One part will broaden the students' knowledge of statistical inference gained in MAS2901 by introducing the linear model. This will start with a simple regression for a scalar covariate, moving to an introductory treatment of a matrix-based approach for a model with more covariates. The other part will be to use the Poisson process as an example of a model for a process of events occurring randomly in time. The main properties of the homogenous Poisson process will be derived, and necessary tools, such as probability and moment generating functions, will be studied.

Outline Of Syllabus

Simple linear regression, i.e. E(Y) = β0 + β1 x for scalar x with Normal errors with unknown variance. Equivalence of least squares and maximum likelihood. Properties of estimator of β = (β0 β1). Introduction of the general linear model using matrix formulation; demonstration of formula for the estimator of β; use of formula for the variance of the estimator of β but no proof. Examples using regression with two or three continuous covariates.

Introduction to PGFs and MGFs. Formal definition of the homogenous Poisson Process. Distribution of number of events in an interval. Distribution of inter-arrival times and time to nth event. Reinforcement of results using simulation.

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 ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Guided Independent StudyAssessment preparation and completion16:006:00Revision for class test
Scheduled Learning And Teaching ActivitiesDrop-in/surgery41:004:00Tutorials in the lecture room
Guided Independent StudyIndependent study123:0023:00Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study33:009:00Review of coursework assignments and course test
Guided Independent StudyIndependent study26:0012:00Preparation for coursework assignments
Total100:00
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.

Assessment Methods

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

Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A85N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M8Coursework assignments
Prob solv exercises2M7Course test
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 one written assignment (approximately 3%) and a small project (approximately 5%). The coursework assignments and the (in class) 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.

Reading Lists

Timetable