The theoretical statistics major provides the mathematical underpinnings of modern statistical practices of estimation, inference and prediction. The major explores both classical approaches to estimation and testing, such as maximum likelihood and the frequentist approach, as well as Bayesian methods that have become ubiquitous parts of modern data analysis. The major covers the theory needed to understand statistical modelling through a variety of lenses: parametric, non-parametric, large-sample theory, small-sample behavior, robustness, and the use of prior information.  

Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Explain the notion of a parametric model, point estimation of the parameters of those models, including maximum likelihood estimation, and inference in simple statistical models with several parameters.  

2. Understand approaches to include a measure of accuracy for estimation procedures and our confidence in them, and apply them to interval estimation.

3. Understand and apply methods of hypothesis testing to assess the plausibility of pre-specified ideas about the parameters of a model.

4. Explain and apply the ideas of non-parametric statistics, wherein estimation and analysis techniques are developed that are not heavily dependent on the specification of an underlying parametric model.

5. Understand the basic concepts of robust estimation in statistics, be able to derive influence functions of simple estimators and use them to evaluate the robustness of estimators.

6. Understand and explain the different uses of randomisation in statistics.

7. Develop, describe analytically and implement common probability models in the Bayesian framework, interpret the results of a Bayesian analysis and perform Bayesian model evaluation and assessment.

8. Appreciate the role of the prior distribution in Bayesian inference, and in particular the use of non-informative priors and conjugate priors.

9. Recognise the need to fit hierarchical models and provide the technical specifications for such models.

10. Understand various important concepts in forecasting and different approaches for modelling trend, seasonality and persistence.

11. Tailor-make models for specific applications and use them to produce forecasts.

Relevant Degrees

• Bachelor of Statistics (BSTAT)