STAT4023: Semester 2, 2021

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Units STAT4023 Semester 2 2021 [Normal day]

Unit of study_

STAT4023: Theory and Methods of Statistical Inference

Semester 2, 2021 [Normal day] - Camperdown/Darlington, Sydney

Overview

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.

Unit details and rules

Unit code	STAT4023
Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prohibitions ?	STAT3013 or STAT3913 or STAT3023 or STAT3923
Prerequisites ?	None
Corequisites ?	None
Assumed knowledge ?	STAT2X11 and (DATA2X02 or STAT2X12) or equivalent. That is, a grounding in probability theory and a good knowledge of the foundations of applied statistics.
Available to study abroad and exchange students	Yes

Teaching staff

Coordinator	Michael Stewart, michael.stewart@sydney.edu.au

Type	Description	Weight	Due	Length
Final exam (Take-home short release)	Final Exam Final exam	55%	Formal exam period	2 hours
Outcomes assessed:
Assignment	Computer reports Lap report	10%	Multiple weeks	n/a
Outcomes assessed:
Online task	Quiz Week 5 Short answers	10%	Week 05	50 min
Outcomes assessed:
Online task	Computer Quiz Computer quiz	10%	Week 12	1 hour
Outcomes assessed:
Online task	Quiz Week 13 Short answers	10%	Week 13	50 min
Outcomes assessed:
Small continuous assessment	Homework Written responses	5%	Weekly	Weekly
Outcomes assessed:
= Type D final exam ?

Assessment summary

Quizzes: you must take your quiz in the tutorial/workshop class in which you are enrolled, unless specific permission to do otherwise is obtained beforehand.

Assessment criteria

The University awards common result grades, set out in the Coursework Policy 2014 (Schedule 1).

As a general guide, a high distinction indicates work of an exceptional standard, a distinction a very high standard, a credit a good standard, and a pass an acceptable standard.

For more information see sydney.edu.au/students/guide-to-grades.

For more information see guide to grades.

Late submission

In accordance with University policy, these penalties apply when written work is submitted after 11:59pm on the due date:

Deduction of 5% of the maximum mark for each calendar day after the due date.
After ten calendar days late, a mark of zero will be awarded.

Academic integrity

The Current Student website provides information on academic integrity and the resources available to all students. The University expects students and staff to act ethically and honestly and will treat all allegations of academic integrity breaches seriously.

We use similarity detection software to detect potential instances of plagiarism or other forms of academic integrity breach. If such matches indicate evidence of plagiarism or other forms of academic integrity breaches, your teacher is required to report your work for further investigation.

You may only use artificial intelligence and writing assistance tools in assessment tasks if you are permitted to by your unit coordinator, and if you do use them, you must also acknowledge this in your work, either in a footnote or an acknowledgement section.

Studiosity is permitted for postgraduate units unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission.

Learning support

Simple extensions

If you encounter a problem submitting your work on time, you may be able to apply for an extension of five calendar days through a simple extension.  The application process will be different depending on the type of assessment and extensions cannot be granted for some assessment types like exams.

Special consideration

If exceptional circumstances mean you can’t complete an assessment, you need consideration for a longer period of time, or if you have essential commitments which impact your performance in an assessment, you may be eligible for special consideration or special arrangements.

Special consideration applications will not be affected by a simple extension application.

Using AI responsibly

Co-created with students, AI in Education includes lots of helpful examples of how students use generative AI tools to support their learning. It explains how generative AI works, the different tools available and how to use them responsibly and productively.

Weekly schedule

WK	Topic	Learning activity
Week 01	Moment-generating functions and applications	Block teaching (5 hr)
Week 02	Multivariate distributions	Block teaching (5 hr)
Week 03	Transformations and of random vectors	Block teaching (5 hr)
Week 04	Exponential families and properties	Block teaching (5 hr)
Week 05	Minimum variance unbiased estimation	Block teaching (5 hr)
Week 06	Most powerful tests	Block teaching (5 hr)
Week 07	Statistical decision theory; simple prediction problems	Block teaching (5 hr)
Week 08	Bayes risk and Bayes decision rules	Block teaching (5 hr)
Week 09	Minimax decision rules	Block teaching (5 hr)
Week 10	Examples in testing, estimation, model selection	Block teaching (5 hr)
Week 11	(Locally) asymptotically minimax procedures	Block teaching (5 hr)
Week 12	Examples of (locally) asymptotically minimax procedures	Block teaching (5 hr)

Study commitment

Typically, there is a minimum expectation of 1.5-2 hours of student effort per week per credit point for units of study offered over a full semester. For a 6 credit point unit, this equates to roughly 120-150 hours of student effort in total.

Learning outcomes

Learning outcomes are what students know, understand and are able to do on completion of a unit of study. They are aligned with the University's graduate qualities and are assessed as part of the curriculum.

Outcomes
Graduate qualities

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.

Graduate qualities

The graduate qualities are the qualities and skills that all University of Sydney graduates must demonstrate on successful completion of an award course. As a future Sydney graduate, the set of qualities have been designed to equip you for the contemporary world.

GQ1	Depth of disciplinary expertise Deep disciplinary expertise is the ability to integrate and rigorously apply knowledge, understanding and skills of a recognised discipline defined by scholarly activity, as well as familiarity with evolving practice of the discipline.
GQ2	Critical thinking and problem solving Critical thinking and problem solving are the questioning of ideas, evidence and assumptions in order to propose and evaluate hypotheses or alternative arguments before formulating a conclusion or a solution to an identified problem.
GQ3	Oral and written communication Effective communication, in both oral and written form, is the clear exchange of meaning in a manner that is appropriate to audience and context.
GQ4	Information and digital literacy Information and digital literacy is the ability to locate, interpret, evaluate, manage, adapt, integrate, create and convey information using appropriate resources, tools and strategies.
GQ5	Inventiveness Generating novel ideas and solutions.
GQ6	Cultural competence Cultural Competence is the ability to actively, ethically, respectfully, and successfully engage across and between cultures. In the Australian context, this includes and celebrates Aboriginal and Torres Strait Islander cultures, knowledge systems, and a mature understanding of contemporary issues.
GQ7	Interdisciplinary effectiveness Interdisciplinary effectiveness is the integration and synthesis of multiple viewpoints and practices, working effectively across disciplinary boundaries.
GQ8	Integrated professional, ethical, and personal identity An integrated professional, ethical and personal identity is understanding the interaction between one’s personal and professional selves in an ethical context.
GQ9	Influence Engaging others in a process, idea or vision.

Outcome map

Learning outcomes	Graduate qualities
Learning outcomes

Responding to student feedback

This section outlines changes made to this unit following staff and student reviews.

This is the first time this unit has been offered

Additional information

Disclaimer

The University reserves the right to amend units of study or no longer offer certain units, including where there are low enrolment numbers.

To help you understand common terms that we use at the University, we offer an online glossary.

Current students

Overview

Overview

Unit details and rules

Teaching staff

Assessment

Assessment

Assessment summary

Assessment criteria

Late submission

Academic integrity

Learning support

Learning support

Simple extensions

Special consideration

Using AI responsibly

Weekly schedule

Weekly schedule

Study commitment

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Disclaimer

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