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Unit of study_

STAT3923: Statistical Inference (Advanced)

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

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

Unit code STAT3923
Academic unit Mathematics and Statistics Academic Operations
Credit points 6
Prohibitions
? 
STAT3913 or STAT3013 or STAT3023
Prerequisites
? 
STAT2X11 and a mark of 65 or greater in (DATA2X02 or STAT2X12)
Corequisites
? 
None
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
Final exam (Take-home short release) Type D final exam Final exam
Final exam
55% Formal exam period 2 hours
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8
Assignment Computer reports
Lab report
10% Multiple weeks Variable
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7
Online task Quiz Week 5
Short answer questions
10% Week 05 50 min
Outcomes assessed: LO1 LO8 LO3 LO2
Online task Computer Quiz
Computer quiz
10% Week 12 1 hour
Outcomes assessed: LO1 LO7 LO6 LO5 LO4 LO3 LO2
Online task Quiz Week 13
Short answer
10% Week 13 50 min
Outcomes assessed: LO1 LO8 LO7 LO6 LO5 LO4 LO3 LO2
Assignment Homework
Written responses
5% Weekly Weekly
Outcomes assessed: LO1 LO2 LO3 LO4 LO5 LO6 LO7 LO8
Type D final exam = Type D final exam ?

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 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.

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.

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 No Description 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 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.

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
GQ1 GQ2 GQ3 GQ4 GQ5 GQ6 GQ7 GQ8 GQ9

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 
  • 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.

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