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During 2021 we will continue to support students who need to study remotely due to the ongoing impacts of COVID-19 and travel restrictions. Make sure you check the location code when selecting a unit outline or choosing your units of study in Sydney Student. Find out more about what these codes mean. Both remote and on-campus locations have the same learning activities and assessments, however teaching staff may vary. More information about face-to-face teaching and assessment arrangements for each unit will be provided on Canvas.

Unit of study_

STAT3923: Statistical Inference (Advanced)

In today's data-rich world more and more people from diverse fields are needing to perform statistical analyses and indeed more and more tools for doing so are becoming available; it is relatively easy to point and click and obtain some statistical analysis of your data. But how do you know if any particular analysis is indeed appropriate? Is there another procedure or workflow which would be more suitable? Is there such thing as a best possible approach in a given situation? All of these questions (and more) are addressed in this unit. You will study the foundational core of modern statistical inference, including classical and cutting-edge theory and methods of mathematical statistics with a particular focus on various notions of optimality. The first part of the unit covers various aspects of distribution theory which are necessary for the second part which deals with optimal procedures in estimation and testing. The framework of statistical decision theory is used to unify many of the concepts. You will rigorously prove key results and apply these to real-world problems in laboratory sessions. By completing this unit you will develop the necessary skills to confidently choose the best statistical analysis to use in many situations.

Code STAT3923
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites:
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STAT2X11 and a mark of 65 or greater in (DATA2X02 or STAT2X12)
Corequisites:
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None
Prohibitions:
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STAT3913 or STAT3013 or STAT3023

At the completion of this unit, you should be able to:

  • LO1. deduce the (limiting) distribution of sums of random variables using moment-generating functions
  • LO2. derive the distribution of a transformation of two (or more) continuous random variables
  • LO3. derive marginal and conditional distributions associated with certain multivariate distributions
  • LO4. classify many common distributions as belonging to an exponential family
  • LO5. derive and implement maximum likelihood methods in various estimation and testing problems
  • LO6. formulate and solve various inferential problems in a decision theory framework
  • LO7. derive and apply optimal procedures in various problems, including Bayes rules, minimax rules, minimum variance unbiased estimators and most powerful tests
  • LO8. rigorously prove the key mathematical results on which the studied methods are based.

Unit outlines

Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.