Matrix Algebra and Linear Models (BIOM4003)


In order to obtain a deeper understanding of statistics it is necessary to learn more about matrices as used to develop and explain statistical and mathematical concepts. Matrices are not just used in statistics: they find use in mathematical models in biology (e.g. age structured population growth models), engineering (e.g. structural perturbation analysis), and economic models (e.g. decision analysis). There are two aims to this unit. Firstly, we will revise matrices learnt in earlier units and then introduce new concepts such as special matrices (symmetric, orthogonal, idempotent), rank, eigenvalues and eigenvectors, as well as some matrix and vector calculus. The second aim is to apply these techniques to the formulation of linear models and linear mixed models which have been introduced in earlier units. In this unit the underlying theory will be developed along with more advanced applications. Furthermore, the students will be introduced to R, an open source statistical software package.

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6 x 1 day workshops.


2 assessment tasks (2x30%), exam (40%)


Textbooks: None. Many reference books such as: Draper, N.R., and Smith, H. (1981). Applied Regression Analysis. Second edition. N.Y.: Wiley. Graybill, F.A. (1969). Introduction to Matrices with Applications in Statistics. Belmont: Wadsworth. Harville

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