## Department of Mathematical Sciences, Unit Catalogue 2008/09

#### MA40198 Statistics for biological dynamic modelling

 Credits: 6
 Level: Masters
 Semester: 2
 Assessment: CW 40%, EX 60%
 Requisites:
 Before taking this unit you must take MA20033
 or an equivalent unit from another institution. Aims: To provide students with an introduction to some of the key quantitative methods available for combining models of biological mechanisms with data, in order to make inferences and predictions about the system that 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 sensible parameterized version of the model. They should be able to maximise this likelihood using R, compare alternative models appropriately, find approximate confidence intervals for model parameters and check the model 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 as a mixture of lectures and computer labs in roughly equal proportion. The lab work will be based on applying the methods to simple, but real biological systems: for example, lab data on Daphnia and blowfly populations; fisheries growth data; forest insect population data; yeast culture data etc. 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 and careful parameter choice; large sample results for ML estimates; distribution, null hypothesis testing, interval estimation; model comparison; AIC an alternative for model comparison; model checking; bootstrapping for uncertainty estimation and to aid optimisation. The second part will look at methods that deal with process error as well as measurement error: process error and random effects; linear mixed effects models; Laplace approximation methods; Bayesian formulation; Stochastic simulation methods.