Department of Mathematical Sciences, Unit Catalogue 2011/12 

Credits:  6 
Level:  Masters UG & PG (FHEQ level 7) 
Period: 
Semester 2 
Assessment:  CW 40%, EX 60% 
Supplementary Assessment:  Likeforlike reassessment (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 combining mechanism based models with 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 nonlinear dynamic model of a system, together with appropriate data, and write down the likelihood for a sensibly parameterized 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: Using statistical package R (T, A); fitting nonlinear models to data (T, 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, pharmecokinetic systems and biological growth models. The first part of the course will deal only with models in which the major stochastic component is measurement error: models as statistical models; the R system for statistical computing; likelihood as a useful measure of fit; ideas of maximum likelihood estimation; practical MLE; nonlinear optimisation; large sample results for ML estimates; hypothesis testing; interval estimation; model comparison; AIC as an alternative for model comparison; model checking. The second part will look at methods that deal with process error as well as measurement error: process error and random effects; Laplace approximation methods; Bayesian formulation; Stochastic simulation methods. 
Programme availability: 
MA40198 is Compulsory on the following programmes:Department of Mathematical Sciences
MA40198 is Optional on the following programmes:Department of Biology & Biochemistry
