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Unit of study_

STAT4023: Theory and Methods of Statistical Inference

In today's data-rich world, more and more people from diverse fields need to perform statistical analyses, and indeed there are more and more tools to do this 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 a 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 aspects of distribution theory which are applied in 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 that are introduced in this unit. 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 STAT4023
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prerequisites:
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None
Corequisites:
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None
Prohibitions:
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STAT3013 or STAT3913 or STAT3023 or STAT3923
Assumed knowledge:
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STAT2X11 and (DATA2X02 or STAT2X12) or equivalent. That is, a grounding in probability theory and a good knowledge of the foundations of applied statistics

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.