STAT3923: Semester 2, 2023

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Units STAT3923 Semester 2 2023 [Normal day]

Unit outline_

STAT3923: Statistical Inference (Advanced)

Semester 2, 2023 [Normal day] - Camperdown/Darlington, Sydney

Overview

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

Academic unit	Mathematics and Statistics Academic Operations
Credit points	6
Prerequisites ?	STAT2X11 and a mark of 65 or greater in (DATA2X02 or STAT2X12)
Corequisites ?	None
Prohibitions ?	STAT3913 or STAT3013 or STAT3023
Assumed knowledge ?	None
Available to study abroad and exchange students	Yes

Teaching staff

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

Type	Description	Weight	Due	Length
Supervised exam ?	Final exam Final exam	55%	Formal exam period	2 hours
Outcomes assessed:
Small continuous assessment	Computer reports Lab report	10%	Multiple weeks	Variable
Outcomes assessed:
Small test	Quiz Week 5 Short answer questions	10%	Week 05 Due date: 30 Aug 2023 at 15:00 Closing date: 30 Aug 2023	50 min
Outcomes assessed:
Small test	Quiz Week 13 Short answer	10%	Week 13 Due date: 30 Oct 2023 at 15:00 Closing date: 30 Oct 2023	50 min
Outcomes assessed:
Online task	Computer Quiz Computer quiz	10%	Week 13 Due date: 01 Nov 2023 at 15:00 Closing date: 01 Nov 2023	1 hour
Outcomes assessed:
Small continuous assessment	Homework Written responses	5%	Weekly	Weekly
Outcomes assessed:

Assessment summary

Quiz: You must sit for the quiz during the tutorial/workshop in which you are enrolled, unless you have explicitly obtained permission to do so beforehand.

Detailed information for each assessment can be found on Canvas.

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 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.

Use of generative artificial intelligence (AI) and automated writing tools

You may only use generative AI and automated writing tools in assessment tasks if you are permitted to by your unit coordinator. If you do use these tools, you must acknowledge this in your work, either in a footnote or an acknowledgement section. The assessment instructions or unit outline will give guidance of the types of tools that are permitted and how the tools should be used.

Your final submitted work must be your own, original work. You must acknowledge any use of generative AI tools that have been used in the assessment, and any material that forms part of your submission must be appropriately referenced. For guidance on how to acknowledge the use of AI, please refer to the AI in Education Canvas site.

The unapproved use of these tools or unacknowledged use will be considered a breach of the Academic Integrity Policy and penalties may apply.

Studiosity is permitted unless otherwise indicated by the unit coordinator. The use of this service must be acknowledged in your submission as detailed on the Learning Hub’s Canvas page.

Outside assessment tasks, generative AI tools may be used to support your learning. The AI in Education Canvas site contains a number of productive ways that students are using AI to improve their learning.

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	Lecture and tutorial (5 hr)
Week 02	Multivariate distributions	Lecture and tutorial (5 hr)
Week 03	Transformations and of random vectors	Lecture and tutorial (5 hr)
Week 04	Exponential families and properties	Lecture and tutorial (5 hr)
Week 05	Minimum variance unbiased estimation	Lecture and tutorial (5 hr)
Week 06	Most powerful tests	Lecture and tutorial (5 hr)
Week 07	Statistical decision theory; simple prediction problems	Lecture and tutorial (5 hr)
Week 08	Bayes risk and Bayes decision rules	Lecture and tutorial (5 hr)
Week 09	Minimax decision rules	Lecture and tutorial (5 hr)
Week 10	Examples in testing, estimation, model selection	Lecture and tutorial (5 hr)
Week 11	(Locally) asymptotically minimax procedures	Lecture and tutorial (5 hr)
Week 12	Examples of (locally) asymptotically minimax procedures	Lecture and tutorial (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.

Required readings

All readings for this unit can be accessed through the Library eReserve, available on Canvas.

I. Miller and M. Miller, John E. Freund’s Mathematical Statistics with Applications, 8th Edition, Pearson, 2014.

Some more advanced but useful references are

I. A. Ibragimov and R. Z. Has’minskii, Statistical Estimation – Asymptotic Theory, Springer, New York, 1981.
E. L. Lehmann and J. P. Romano, Testing Statistical Hypotheses, 3rd edition, Springer, New York, 2005.

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.

No changes have been made since this unit was last offered.

Additional information

Work, health and safety

We are governed by the Work Health and Safety Act 2011, Work Health and Safety Regulation 2011 and Codes of Practice. Penalties for non-compliance have increased. Everyone has a responsibility for health and safety at work. The University’s Work Health and Safety policy explains the responsibilities and expectations of workers and others, and the procedures for managing WHS risks associated with University activities.

General Laboratory Safety Rules

No eating or drinking is allowed in any laboratory under any circumstances
A laboratory coat and closed-toe shoes are mandatory
Follow safety instructions in your manual and posted in laboratories
In case of fire, follow instructions posted outside the laboratory door
First aid kits, eye wash and fire extinguishers are located in or immediately outside each laboratory
As a precautionary measure, it is recommended that you have a current tetanus immunisation. This can be obtained from University Health Service: unihealth.usyd.edu.au/

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

Required readings

Learning outcomes

Learning outcomes

Graduate qualities

Outcome map

Responding to student feedback

Responding to student feedback

Additional information

Additional information

Work, health and safety

Disclaimer

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