Unit of study_

# STAT4023: Theory and Methods of Statistical Inference

## 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.

### Details

Academic unit Mathematics and Statistics Academic Operations STAT4023 Theory and Methods of Statistical Inference Semester 2, 2022 Normal day Remote 6

### Enrolment rules

 Prohibitions ? STAT3013 or STAT3913 or STAT3023 or STAT3923 None None STAT2X11 and (DATA2X02 or STAT2X12) or equivalent. That is, a grounding in probability theory and a good knowledge of the foundations of applied statistics Yes

### Teaching staff and contact details

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

## Assessment

Type Description Weight Due Length
Final exam (Record+) Final Exam
Final exam
55% Formal exam period 2 hours
Outcomes assessed:
Small continuous assessment Computer reports
Lap report
10% Multiple weeks n/a
Outcomes assessed:
10% Week 05 50 min
Outcomes assessed:
Computer quiz
10% Week 12 1 hour
Outcomes assessed:
10% Week 13 50 min
Outcomes assessed:
Small continuous assessment Homework
Written responses
5% Weekly Weekly
Outcomes assessed:
= Type B final exam
• 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.

### 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.

### Special consideration

If you experience short-term circumstances beyond your control, such as illness, injury or misadventure or if you have essential commitments which impact your preparation or performance in an assessment, you may be eligible for special consideration or special arrangements.

The Current Student website provides information on academic honesty, academic dishonesty, 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 dishonesty or plagiarism seriously.

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

## Weekly schedule

WK Topic Learning activity Learning outcomes
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.

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.

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.