STATS 730 : Statistical Inference
2022 Semester Two (1225) (15 POINTS)
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 increasing focus on applications as the course progresses. 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, 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. Prior familiarity with R is strongly advised for those undertaking this course.
Capabilities Developed in this Course
|Capability 1:||Disciplinary Knowledge and Practice|
|Capability 2:||Critical Thinking|
|Capability 3:||Solution Seeking|
|Capability 4:||Communication and Engagement|
|Capability 5:||Independence and Integrity|
- Critically evaluate point estimators in regard to the properties of mean squared error, sufficiency, ancillarity, uniformly minimum variance unbiasedness, and asymptotic efficiency. (Capability 1 and 2)
- Use and apply maximum likelihood as a tool for statistical inference (Capability 1 and 2)
- Apply frequentist likelihood-based inference methods (Capability 1 and 3)
- Learn and apply advanced likelihood-based techniques (Capability 1, 2, 3 and 4)
- Be able to produce portable code to maximise complex likelihoods. (Capability 1, 3, 4 and 5)
|Final Exam||55%||Individual Examination|
|Assessment Type||Learning Outcome Addressed|
A minimum pass mark of 50% (or 27.5/55) on the Final Exam is required to pass this course.
Properties of point estimators
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.
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.
The delivery mode of this course may change in accordance with changes to New Zealand Government recommendations. Updates for this course will be provided on the course Canvas page.
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- Lecture slides
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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.