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APTS module: Statistical Modelling

Module leader: H Ogden

Please see the full Module Specifications for background information relating to all of the APTS modules, including how to interpret the information below.

Aim: To introduce important aspects of statistical modelling, including model selection, various extensions to generalised linear models, and non-linear models.

Learning outcomes: After taking this module, students should be able to:

  • Provide a theoretical justification for the use of various criteria for model selection, and apply these techniques in practice.
  • Describe some reasons why Generalised Linear Models may fail to fit real data well, and apply techniques to diagnose such failures.
  • Describe some commonly-used extensions to Generalised Linear Models, and conduct frequentist and Bayesian inference for these models.

Prerequisites: Preparation for this module should (re-)establish familiarity with linear and generalized linear models, and with likelihood and Bayesian inference. Students who are familiar with (for example) chapters 4, 8, 10 and 11 of Davison (2003) ``Statistical Models'' will be very well prepared (and will already know something of the areas to be covered in the module).

Topics:

  • Principles and practice of model selection;
  • Extensions of the Generalised Linear Model, including models for overdispersion and mixed-effects models;
  • Non-linear models.

Assessment: Exercises set by the module leader, which will include some practical data analysis and statistical modelling.

Further reading:

  • Davison (2003). Statistical Models.
  • Gelman and Hill (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models.