Student Records
Programme & Unit Catalogues

## MA40198: Applied statistical inference

Owning Department/School: Department of Mathematical Sciences
Credits: 6
Level: Masters UG & PG (FHEQ level 7)
Period: Semester 2
Assessment: CW 40%, EX 60%
Supplementary Assessment: Mandatory Extra Work (where allowed by programme regulations)
Requisites: Before taking this unit you must take MA20226 or an equivalent unit from another institution. In particular, some familiarity with R statistical package, basic probability and maximum likelihood estimation are assumed.
Description: Aims:
To provide students with an introduction to some of the key quantitative methods available for making statistical inferences about non-standard and non-linear models from data, in order to make inferences and predictions about the system that the data and model relate to.

Learning Outcomes:
By the end of the course students should be able to take a simple non-standard and non-linear model of a system, together with appropriate data, and write down the likelihood for a sensibly parameterised version of the model. They should be able to maximise this likelihood, or use it as part of a Bayesian analysis, with R. In addition students should be able to compare alternative models appropriately, find approximate confidence intervals for model parameters and check models critically. Students should be able to handle simple stochastic model variants via approximate likelihood based methods, or stochastic simulation.

Skills:
Numeracy T/F A
Problem Solving T/F A
Written Communication F (in tutorials), A

Content:
The course will be delivered via 1 lecture and 2 computer labs per week. The lab work will be based on applying the methods to simple, but real non-linear systems: for example, pest insect populations, chemostat dynamics, pharmaco-kinetic systems and biological growth models.
The course will cover:
* Basics of large sample theory of maximum likelihood estimation.
* Basics of numerical optimization.
* Use of numerical optimization for maximum likelihood estimation in R
* Basics of practical Bayesian approach to inference.
* Basic theory of Markov Chain Monte Carlo
* How to code up simple MCMC samplers in R
* Model checking, criticism and interpretation.
* Random effects in models.
Programme availability:

#### MA40198 is Compulsory on the following programmes:

Department of Mathematical Sciences
• TSMA-AFM08 : MSc Modern Applications of Mathematics (Full-time) - Year 1
• TSMA-AFL02 : PG Dip Modern Applications of Mathematics (Full-time) - Year 1

#### MA40198 is Optional on the following programmes:

Department of Biology & Biochemistry
• RSBB-AFM07 : Integrated PhD Postgenomic Biosciences (Biosciences Route) (Full-time) - Year 1
• TSBB-AFM03 : MRes Biosciences (Full-time) - Year 1
Department of Mathematical Sciences
• USMA-AFB15 : BSc (hons) Mathematical Sciences (Full-time) - Year 3
• USMA-AKB16 : BSc (hons) Mathematical Sciences (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB16 : BSc (hons) Mathematical Sciences with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB13 : BSc (hons) Mathematics (Full-time) - Year 3
• USMA-AKB14 : BSc (hons) Mathematics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AFB01 : BSc (hons) Mathematics and Statistics (Full-time) - Year 3
• USMA-AKB02 : BSc (hons) Mathematics and Statistics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB02 : BSc (hons) Mathematics and Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AAB14 : BSc (hons) Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFB05 : BSc (hons) Statistics (Full-time) - Year 3
• USMA-AKB06 : BSc (hons) Statistics (Full-time with Thick Sandwich Placement) - Year 4
• USMA-AAB06 : BSc (hons) Statistics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 3
• USMA-AFM14 : MMath Mathematics (Full-time) - Year 4
• USMA-AAM15 : MMath Mathematics with Study Year Abroad (Full-time with Study Year Abroad) - Year 4
• TSMA-AFM09 : MSc Mathematical Sciences (Full-time) - Year 1
• TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 1
• TSMA-APM09 : MSc Mathematical Sciences (Part-time) - Year 2

Notes:
* This unit catalogue is applicable for the 2012/13 academic year only. Students continuing their studies into 2013/14 and beyond should not assume that this unit will be available in future years in the format displayed here for 2012/13.
* Programmes and units are subject to change at any time, in accordance with normal University procedures.
* Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.