
Academic Year:  2012/3 
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 nonstandard and nonlinear 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 nonstandard and nonlinear 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 nonlinear systems: for example, pest insect populations, chemostat dynamics, pharmacokinetic 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
MA40198 is Optional on the following programmes:Department of Biology & Biochemistry
