To present the fundamental principles of statistical inference, starting from the likelihood and the large sample results that are widely used in practice, as well as introducing methods of modern Bayesian inference, with an emphasis on practical issues and applications

Lectures: 40 hours (2 hours per week over two semesters)

Tutorials: 8 hours (over two semesters)

7 2-hour computer-based practical sessions over two semesters

STATS5028 Statistical Inference (Level M)

STATS5014 Bayesian Statistics (Level M

None

60 minute class test (20%) 120-minute, end-of-course examination (80%)

To establish a solid understanding of the fundamental principles of likelihood-based and Bayesian inference that are widely used in practice. To introduce students to the main ideas of modern likelihood-based and Bayesian statistics, and to illustrate formulation and analysis of statistical models in both frameworks, and implementation of these in statistical programming software.

By the end of this course students will be able to:

■ write down the likelihood and perform likelihood-based inference for a variety of statistical models

■ explain the choice of prior distribution and describe the rules for updating prior distributions in the presence of data, and for calculating posterior predictive distributions

■ maximise likelihoods through numerical methods

■ summarise model results using point and interval estimates for both likelihood and Bayesian frameworks

■ test hypotheses about likelihood model parameters, and calculate power

■ describe key theoretical properties that measure the effectiveness of procedures for point estimation, testing and interval estimation and the extent to which likelihood based methods possess such properties

■ discuss the principles behind the bootstrap and apply this technique to practical problems

■ formulate and analyse likelihood and Bayesian models using statistical programming language