# Current students

Unit of study_

### 2025 unit information

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.

## Unit details and rules

#### Science

 Prerequisites: ? STAT2X11 and a mark of 65 or greater in (DATA2X02 or STAT2X12) None STAT3913 or STAT3013 or STAT3023 None

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 availability

This section lists the session, attendance modes and locations the unit is available in. There is a unit outline for each of the unit availabilities, which gives you information about the unit including assessment details and a schedule of weekly activities.

The outline is published 2 weeks before the first day of teaching. You can look at previous outlines for a guide to the details of a unit.

Session MoA   Location Outline
Semester 2 2024
Normal day Camperdown/Darlington, Sydney
Session MoA   Location Outline
Semester 2 2025
Normal day Camperdown/Darlington, Sydney
Outline unavailable
Session MoA   Location Outline
Semester 2 2020
Normal day Camperdown/Darlington, Sydney
Semester 2 2021
Normal day Camperdown/Darlington, Sydney
Semester 2 2021
Normal day Remote
Semester 2 2022
Normal day Camperdown/Darlington, Sydney
Semester 2 2022
Normal day Remote
Semester 2 2023
Normal day Camperdown/Darlington, Sydney

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### Modes of attendance (MoA)

This refers to the Mode of attendance (MoA) for the unit as it appears when you’re selecting your units in Sydney Student. Find more information about modes of attendance on our website.