Unit of study_

STAT3023: Statistical Inference

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 a thing as the 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 apply the methods learnt 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 STAT3023 Mathematics and Statistics Academic Operations 6 STAT3913 or STAT3013 or STAT3923 STAT2X11 None DATA2X02 or STAT2X12 Yes

Teaching staff

Coordinator Rachel Wang, rachel.wang@sydney.edu.au Rachel Wang Linh Nghiem

Assessment

Type Description Weight Due Length
Final exam (Record+) Final exam
Written exam
55% Formal exam period 2 hours
Outcomes assessed:
Small continuous assessment Computer reports
Lab report
10% Multiple weeks Variable
Outcomes assessed:
12.5% Week 05
Due date: 31 Aug 2022 at 15:00
50 min
Outcomes assessed:
12.5% Week 11
Due date: 19 Oct 2022 at 15:00
50 min
Outcomes assessed:
Computer quiz
10% Week 13
Due date: 02 Nov 2022 at 15:00
1 hour
Outcomes assessed:
= Type B final exam

Assessment summary

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.

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.

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 Learning outcomes
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.

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.

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.

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.

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

GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

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.

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