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
- 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.
- Demonstrate an understanding of approaches to include a measure of accuracy for estimation procedures and our confidence in them, and apply them to interval estimation.
- 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.
- Using a diverse range of discipline backgrounds and varied data, communicate the role of generalised linear modelling techniques (GLMs) in modern applied statistics and implement GLM methodology.
- 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 in a variety of discipline settings.
- Demonstrate an understanding of 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.
- Demonstrate an understanding of various important concepts in forecasting and different approaches for modelling trend, seasonality and persistence.
Other Information
Students will need to complete all of the following courses to be able to complete the 48 units of this major:
- MATH1013 OR MATH1115 OR MATH1113
- MATH1014 OR MATH1116 (MATH1014 or MATH1116 is only required if MATH1113 not completed)
- STAT1003 OR STAT1008 (may be included in the 12 units from completion of further courses from the subject area STAT Statistics)
- STAT2001 OR STAT2013 (may be included in the 12 units from completion of further courses from the subject area STAT Statistics)
- STAT2008 OR STAT2014 (may be included in the 12 units from completion of further courses from the subject area STAT Statistics)
Requirements
This major requires the completion of 48 units, which must include:
30 units from completion of the following compulsory courses:
EMET3007 Business and Economic Forecasting
STAT3013 Statistical Inference
STAT3015 Generalised Linear Modelling
STAT3016 Introduction to Bayesian Data Analysis
STAT3056 Advanced Mathematical Statistics
6 units from completion of 2000-level courses from the subject area MATH Mathematics
12 units from completion of further courses from the subject area STAT Statistics
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