STATS 730 : Statistical Inference
Science
2025 Semester Two (1255) (15 POINTS)
Course Prescription
Course Overview
STATS 730 consists of interactive lectures covering classical and advanced aspects of statistical inference and individually assigned research projects to be presented in class. The lecture component consists in an introduction to simple maximum likelihood concepts is followed by a discussion of point estimators, including methods to find them and key properties such as mean squared error, sufficiency, ancillarity, and unbiasedness. (Asymptotic efficiency is also discussed in the second half of the course.) The Halmos-Savage, Rao-Blackwell and Cramér-Rao theorem are discussed and applied. This segment is followed by an in-depth consideration of the likelihood-based frequentist approach to inference. Simple and not-so-simple (e.g., finite mixture model) examples based on independent and identically distributed samples are presented. The essential properties, concepts and tools of maximum-likelihood inference are then presented, with an equal focus on theory, such as asymptotic evaluations, and on applications. Maximum likelihood and extensions are applied in a wide variety of settings with examples in R, with special attention to exponential families applied to generalised linear modelling. The course concludes by looking at extensions of maximum likelihood for models for more challenging situations, including quasi-likelihood and conditional likelihood.
The research component consists in an assigned project to be completed in two phases, based on an assigned topic, a research question and a given data set: 1) a literature review and description of the methods to be applied to answer the research question using the data; 2) the results of the analysis. Each phase will be presented by the students, and be the object of an assessed in-class quiz co-created by the presenting students and the instructors. The topics involved will be varied and current, some of them taken from methods for dependent data, survival analysis, methods to handle missing data, predictive analytics, causal inference, semi-parametric inference, and others.
Prior familiarity with R is strongly advised for those undertaking this course.
Capabilities Developed in this Course
| Capability 1: | People and Place |
| Capability 3: | Knowledge and Practice |
| Capability 4: | Critical Thinking |
| Capability 5: | Solution Seeking |
| Capability 6: | Communication |
| Capability 7: | Collaboration |
| Capability 8: | Ethics and Professionalism |
Learning Outcomes
- Critically evaluate point estimators, interval/set estimators and tests statistics in regard to their small-sample and asymptotic statistical properties. (Capability 3 and 4)
- Use and apply maximum likelihood and its extensions as tools for statistical inference. (Capability 3, 4 and 5)
- Create and follow an appropriate workflow for a data analytical project. (Capability 3, 4 and 5)
- Understand and apply methods for statistical inference in the presence of data dependence, censoring and missingness. (Capability 3, 4 and 5)
- Be able to produce portable code to wrangle and analyse data in a reproducible manner. (Capability 3, 4, 5, 6, 7 and 8)
- Effectively and efficiently undertake in-depth research on an assigned topic. (Capability 3, 4, 5, 7 and 8)
- Communicate and explain ideas correctly and effectively in written and oral communication regarding methodology and results. (Capability 1, 4, 6 and 8)
- Carry out a comprehensive literature search. (Capability 3, 6 and 7)
Assessments
| Assessment Type | Percentage | Classification |
|---|---|---|
| In-class tests (2) | 35% | Individual Test |
| Project-related quizzes | 10% | Individual Test |
| Project part 1: literature review and methodology | 20% | Individual Coursework |
| Project part 2: code, results and discussion | 25% | Individual Coursework |
| Project presentations (2) | 10% | Individual Coursework |
| 5 types | 100% |
| Assessment Type | Learning Outcome Addressed | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||
| In-class tests (2) | ||||||||||
| Project-related quizzes | ||||||||||
| Project part 1: literature review and methodology | ||||||||||
| Project part 2: code, results and discussion | ||||||||||
| Project presentations (2) | ||||||||||
Key Topics
- Introduction to likelihood and principles of inference
- Parametric families of distributions, including natural exponential families and exponential dispersion models
- Methods of finding point estimators
- Properties of point estimators
- Essential concepts and iid examples
- Large-sample methods, including hypothesis tests and profile likelihood-based confidence intervals/regions
- Delta-method, critical look at Wald-based inference
- Maximising the likelihood in practice
- Asymptotic evaluations
- Generalised linear models and extensions
- Quasi-likelihood, Generalised estimating equations and Linear mixed models
Special Requirements
The practical work will consist in a report in two parts (literature review and methods, results and discussion) that will each be presented in class and assessed at the end of the first and second half of the semester.
The tests will be held during class time.
The student-project-related quizzes will be held at the end of each presentation.
Workload Expectations
This course is a Level 9 15-point course and students are expected to spend 150 hours per semester involved in each 15-point course that they are enrolled in.
The breakdown is as follows:
- Outside the mid-semester break, a typical weekly workload includes:
- 4 hours of lectures
- 2 hours reviewing the course content
- 5 hours of work on project and/or test preparation
Delivery Mode
Campus Experience
Attendance is expected at scheduled activities to complete components of the course.
Lectures will be available as recordings.
The course will not include live online events.
Attendance on campus is required for the term tests.
The activities for the course are scheduled as a standard weekly timetable.
Learning Resources
Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).
Please remember that the recording of any class on a personal device requires the permission of the instructor.
- Lecture slides will be available on Canvas. The lecture slides, along with the assignment material, will contain all the information needed to undertake the course successfully
- Maximum Likelihood Estimation and Inference, with Examples in R, SAS and ADMB, by Millar RB. (2011). John Wiley & Sons. (The textbook will be available at no cost in PDF format on Canvas)
- Statistical Inference, by Casella G & Berger R. (2002). 2nd ed. Duxbury.
Student Feedback
During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.
At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.
Your feedback helps to improve the course and its delivery for all students.
New course for 2025: student feedback will be taken into account when reviewing the course.
Based on recent student feedback, supplementary examples will be introduced when discussing properties of point estimators, which is a more theoretical topic.
Other Information
The elevation of STATS 730 to level 9 will be trialled for the first time in 2025. Although no assignments are planned as formative assessments, exercises will be handed out and expected to be worked out by the students in preparation for the two class tests.
Academic Integrity
The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework, tests and examinations as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. A student's assessed work may be reviewed against electronic source material using computerised detection mechanisms. Upon reasonable request, students may be required to provide an electronic version of their work for computerised review.
Class Representatives
Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.
Copyright
The content and delivery of content in this course are protected by copyright. Material belonging to others may have been used in this course and copied by and solely for the educational purposes of the University under license.
You may copy the course content for the purposes of private study or research, but you may not upload onto any third party site, make a further copy or sell, alter or further reproduce or distribute any part of the course content to another person.
Inclusive Learning
All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.
Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website http://disability.auckland.ac.nz
Special Circumstances
If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.
If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.
This should be done as soon as possible and no later than seven days after the affected test or exam date.
Learning Continuity
In the event of an unexpected disruption we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.
The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.
Student Charter and Responsibilities
The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html.
Disclaimer
Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.
In this course you may be asked to submit your coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.