This module builds on the material covered in MATH2805 and MATH1805. The theory of statistical hypothesis testing is expanded to include; statistical power and sample size; further application of MGFs leading to a proof of the central limit theorem; likelihood based statistical modelling, estimation and inference; linear statistical modelling including simple and multiple regression and ANOVA.
Statistical Power: Type I and II errors; Operating Characteristic curves, power functions and sample size for estimation.
Properties of moment generating functions (MGF) with specific application to proving the central limit theorem.
Likelihood based model formulation and fitting. Likelihood estimation compared to the method of moments. Likelihood inference for single and multiple parameter cases. Wald based hypothesis testing and confidence intervals. Likelihood ratio tests.
Linear statistical models: simple and multiple regression. ANOVA.
Lectures supported by tutorials and computer lab. sessions.
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