On successful completion of this module students should be able to demonstrate knowledge of the basic parametric models used in statistics and the methods of maximum likelihood and likelihood ratio. They should be able to derive large sample results and identify when they are appropriate. They should demonstrate knowledge of the concepts of profile, marginal and conditional likelihood and why they are necessary. They should be able to explain the delta method, jackknife, the bootstrap and results relating to variability. They should be able to carry out multiple testing procedures including that of Benjamini and Hochberg.They should be able to use the basic tools of classical statistics and demonstrate knowledge of how to use them in modern statistical problems. They should have a basic understanding of Bayesian models and their role in modern statistics.

Maximum likelihood; Invariance; Score statistic; Fisher information; Cramer-Rao lower bound; Large sample results: Central limit theorem, consistency and asymptotic normality of the mle; Likelihood ratio statistics and asymptotic distribution; delta method, jackknife, bootstrap, method of moments, Bayesian estimation; conditional, profile and marginal likelihoods, Fisher's exact test; confidence intervals and coverage probability; multiple testing: Bonferroni, Holm, Benjamini-Hochberg.

A knowledge of probability and statistical inference to the level of Probability Theory STAT20110 and Inferential Statistics STAT20100 courses is required. A knowledge of linear models to the level of STAT30240 is required. Good knowledge of calculus and linear algebra is required.

• Feedback individually to students, post-assessment

Each assignment will be corrected and graded and returned to the student. This will be followed by solutions to the Assignments covered in Tutorials.