MT3508 Applied Statistics

Further information on which modules are specific to your programme.

Module description

Together with MT3507, this module provides a bridge between second year and Honours modules in statistics. It deals with the application of statistical methods to test hypotheses and draw inferences from data, using maximum likelihood methods. The module starts by developing general-purpose maximum likelihood methods, with interval estimation by means of the information matrix and the bootstrap. It goes on to deveop generalised linear models, linear models and analysis of variance models as special cases of maximum likelihood methods. It covers diagnostic methods, including methods for selecting between models, checking assumptions and testing goodness-of-fit. It has an applied focus, with extensive use of R to give students practice in doing inference with real datasets, from problem formulation through to final conclusions.

Intended learning outcomes

• Understand inference by maximum likelihood sufficiently well to conduct maximum likelihood inference on unseen problems using the statistical software R, and to draw appropriate conclusions
• Be able to construct appropriate likelihood functions from non-mathematical problem descriptions, for problems involving uncertainty, and in which observations are independent
• Be able to use R to implement likelihood functions, to maximise them with respect to unknown parameters, and obtain confidence intervals for model parameters and functions of parameters
• Understand the relationships between ANOVA models, linear regression models, generalised linear models, and more general statistical models that do not fall into any of these categories
• Be able to conduct appropriate model selection and diagnostic tests for these models, to assess model adequacy
• Be able to obtain Wald confidence intervals, profile likelihood confidence intervals, and bootstrap confidence intervals for parameters and functions of parameters