# STATS 732 : Foundations of Statistical Inference

## Science

### Course Prescription

Fundamentals of statistical inference including estimation, hypothesis testing, likelihood methods, multivariate distributions, joint, marginal, and conditional distributions, vector random variables, and an introduction to decision theory and Bayesian inference.

### Course Overview

This course gives an introduction to the fundamental theory in statistical inference. The knowledge taught in this course is fundamental in statistical inference and necessary to carry out decent statistical research. The prerequisites are a basic knowledge of probability, statistics and mathematics (Stage 2, basically). It comprises the topics in discrete and continuous random variables, multivariate distributions, sampling theory for the normal distribution, parametric estimation, hypothesis testing, and linear regression models, and statistical decision theory.

### Course Requirements

Prerequisite: STATS 210 or 225, and 15 points from MATHS 208, 250 Restriction: STATS 310

### Capabilities Developed in this Course

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

### Learning Outcomes

By the end of this course, students will be able to:
1. Understand discrete and continuous random variables. (Capability 1)
2. Be able to use calculus to derive formulae for univariate distributions. (Capability 1 and 3)
3. Understand multivariate distributions and can derive marginal and conditional distributions, etc. (Capability 1 and 3)
4. Understand and use the sampling theory for the normal distribution. (Capability 1 and 2)
5. Can use the theory for parameter estimation and find and carry out a likelihood analysis. (Capability 1 and 3)
6. Understand and can derive the formula for hypothesis testing. (Capability 1 and 3)
7. Understand and can use the theory for linear regression and the associated geometry. (Capability 1 and 3)
8. Understand and can use the fundamental decision theory to solve problems. (Capability 1, 2 and 3)

### Assessments

Assessment Type Percentage Classification
Assignments 30% Individual Coursework
Test 20% Individual Test
Final Exam 50% Individual Examination
1 2 3 4 5 6 7 8
Assignments
Test
Final Exam

### Learning Resources

Comprehensive coursebook is available.

Reference book: Rice, J. A. (2007). Mathematical Statistics & Data Analysis (3rd ed.). Duxbury Press.

### Special Requirements

No.

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 3 hours of lectures, two 1-hour tutorials, 3 hours of reading and thinking about the content and 2 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.

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 05/03/2020 09:37 p.m.