STATS 730 : Statistical Inference


2024 Semester Two (1245) (15 POINTS)

Course Prescription

Fundamentals of likelihood-based inference, including sufficiency, conditioning, likelihood principle, statistical paradoxes. Theory and practice of maximum likelihood. Examples covered may include survival analysis, GLM's, nonlinear models, random effects and empirical Bayes models, and quasi-likelihood.

Course Overview

STATS 730 gives you general-purpose skills to model real data, using likelihood-based statistical inference under the frequentist paradigm. A gentle 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 is applied in a wide variety of settings with examples in R. The course concludes by looking at extensions of maximum likelihood for models for more challenging situations, including quasi-likelihood, conditional likelihood, mixed effects modelling and generalised estimating equations. STATS 730 provides the tools and skills used by many other graduate courses on offer in this department, and is of invaluable use to students undertaking MSc projects or beginning PhD study. It gives strong exposure to statistical programming in R. 

Prior familiarity with R is strongly advised for those undertaking this course.

Course Requirements

Prerequisite: STATS 310 or 732

Capabilities Developed in this Course

Capability 3: Knowledge and Practice
Capability 4: Critical Thinking
Capability 5: Solution Seeking
Capability 6: Communication
Capability 7: Collaboration
Graduate Profile: Master of Science

Learning Outcomes

By the end of this course, students will be able to:
  1. Critically evaluate point estimators in regard to the properties of mean squared error, sufficiency, ancillarity, uniformly minimum variance unbiasedness, and asymptotic efficiency. (Capability 3 and 4)
  2. Use and apply maximum likelihood as a tool for statistical inference (Capability 3, 5 and 6)
  3. Apply frequentist likelihood-based inference methods (Capability 3 and 5)
  4. Learn and apply advanced likelihood-based techniques (Capability 3 and 5)
  5. Be able to produce portable code to maximise complex likelihoods. (Capability 3, 4, 6 and 7)


Assessment Type Percentage Classification
Assignments 30% Individual Coursework
Test 20% Individual Test
Final Exam 50% Individual Examination
Assessment Type Learning Outcome Addressed
1 2 3 4 5
Final Exam

A minimum pass mark of 50% (or 25/50) on the Final Exam is required to pass this course.


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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 test will be held during class time.

Workload Expectations

This course is a standard 15-point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.

For this course, a typical weekly workload includes:

  • 3 hours of lectures
  • 3-4 hours of reviewing the course content
  • 6 hours of work on assignments 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 midterm test and exam.
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:
  • 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
Recommended Reading:
  • 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.

Based on recent student feedback, a quiz (not for credit) will be made available in the first week of the class covering some of the prior mathematical and programming knowledge expected of students. Students will then quickly be able to discover whether they are adequately prepared for the course. We also intend to produce self-check quizzes to enable students to monitor their understanding of the material.

Academic Integrity

The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework 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. This requirement also applies to sources on the internet. A student's assessed work may be reviewed for potential plagiarism or other forms of academic misconduct, using computerised detection mechanisms.

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.


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

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

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 course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, 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


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 students may be asked to submit 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. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.

Published on 31/10/2023 10:54 a.m.