## MA40198: Applied statistical inference

[Page last updated: 23 October 2023]

Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 1
Assessment Summary: CW 40%, EX 60%
Assessment Detail:
• Coursework (CW 40%)
• Examination (EX 60%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module 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.
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.

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.

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.

Course availability:

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

Department of Economics
• UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 3)
• UHES-AAB04 : BSc(Hons) Economics and Mathematics with Study year abroad (Year 4)
• UHES-AKB04 : BSc(Hons) Economics and Mathematics with Year long work placement (Year 4)
• UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 4)
Department of Mathematical Sciences
• RSMA-AFM16 : Integrated PhD Statistical Applied Mathematics
• TSMA-AFM17 : MRes Statistical Applied Mathematics
• TSMA-AFM16 : MSc Statistical Applied Mathematics
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 3)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 4)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 4)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 3)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 3)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 4)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 4)
• USMA-AFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 3)
• USMA-AAB06 : BSc(Hons) Statistics with Study year abroad (Year 4)
• USMA-AKB06 : BSc(Hons) Statistics with Year long work placement (Year 4)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 3)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 4)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 4)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 5)

 Notes: This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24. Courses and units are subject to change 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. Find out more about these and other important University terms and conditions here.