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MA40198: Applied statistical inference

Follow this link for further information on academic years Academic Year: 2020/1
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period: Semester 1
Further information on unit assessment Assessment: CW 40%, EX 60%
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites 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.
Further information on descriptions 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.
Further information on programme availabilityProgramme availability:
NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2020

MA40198 is Optional on the following programmes:

Department of Economics
  • UHES-AFB04 : BSc(Hons) Economics and Mathematics (Year 3)
  • UHES-ACB04 : BSc(Hons) Economics and Mathematics with Combined Placement and Study Abroad (Year 4)
  • 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)
Department of Mathematical Sciences
  • 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-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-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 4)
  • USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 4)
  • USMA-AFB05 : BSc(Hons) Statistics (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: