# STATS 730 : Statistical Inference

## Science

### 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 thoughtful consideration of the frequentist approach to inference (compared to Bayesian). Simple and not-so-simple (e.g., finite mixture model) iid examples are presented. The essential properties, concepts and tools of maximum-likelihood inference are then presented. Maximum likelihood is applied in a wide variety of settings with examples in R, and ADMB (and/or TMB) where needed. (Students may choose any of these languages for their homework.) The course concludes by looking at extensions of maximum likelihood for models for more challenging situations, including quasi-likelihood, conditional likelihood, and latent-variable models. STATS 730 provides the tools and skills used by many other graduate courses on offer in this department, and of invaluable use to students undertaking MSc projects or beginning PhD study. It gives strong exposure to statistical programming in R, with extension to use of ADMB (and/or TMB).

### Course Requirements

Prerequisite: STATS 310 or 732

### Capabilities Developed in this Course

 Capability 1: Disciplinary Knowledge and Practice Capability 2: Critical Thinking Capability 3: Solution Seeking Capability 4: Communication and Engagement

### Learning Outcomes

By the end of this course, students will be able to:
1. Use and apply maximum likelihood as a tool for statistical inference (Capability 1 and 2)
2. Apply frequentist likelihood-based inference methods (Capability 1 and 3)
3. Learn and apply advanced likelihood-based techniques (Capability 1, 2, 3 and 4)

### Assessments

Assessment Type Percentage Classification
Assignments 30% Individual Coursework
Test 15% Individual Test
Final Exam 55% Individual Examination
1 2 3
Assignments
Test
Final Exam

Passing requires obtaining a grade of 50% or more on the final examination.

### Key Topics

Introduction to likelihood and principles of inference
Essential concepts and iid examples
Large-sample methodology, including hypothesis tests and confidence intervals/regions
Essential tools and tricks
Maximising the likelihood
Applications
Generalised linear models and extensions
Latent-variable models

### Learning Resources

• Required text book:
Millar RB. (2011). Maximum Likelihood Estimationand Inference, with Examples in R, SAS and ADMB. John Wiley & Sons.
The textbook will be available at no cost in PDF format on Canvas.
• Lecture slides
Available on Canvas

### Special Requirements

No special requirements.

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, you can expect 36 hours of lectures, 40 hours of reading and thinking about the content and 74 hours of work on assignments and/or test preparation.

### Digital 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.

Piazza will be available as a discussion platform for this course. Rather than emailing questions to the instructor, we encourage you to post your questions on Piazza. Emailed or verbal questions may be reposted on Piazza by the instructors so that questions and answers can benefit everyone in the class.

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.

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 against online source material using computerised detection mechanisms.

### 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 at 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.

### 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.

### 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.

Published on 09/07/2020 03:05 p.m.