# Mathematical Statistics

University of Queensland

## Course Description

• ### Course Name

Mathematical Statistics

• ### Host University

University of Queensland

• ### Location

Brisbane, Australia

• ### Area of Study

Mathematics, Statistics

• ### Language Level

Taught In English

• ### Prerequisites

(STAT2004 + MATH2000)

• ### Course Level Recommendations

Upper

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Host University Units

2
• Recommended U.S. Semester Credits
4
• Recommended U.S. Quarter Units
6
• ### Overview

Course Description
Likelihood theory: maximum likelihood, asymptotic theory, nuisance parameters, applications, likelihood ratio test, score tests, Wald tests, exponential family (properties: sufficiency, completeness). Confidence intervals, hypothesis tests. Baysian inference. Multivariate normal distribution & quadratic forms. Distributional results & inference for general linear model.

Course Introduction
Statistics provides the mathematical language and techniques necessary for understanding and dealing with chance, uncertainty and variability in Nature. In this course you will learn how to use probability and other branches of mathematics to extract patterns and other useful information from numerical data in a careful and precise manner. The course has three main parts:
• Classical Mathematical Statistics. Here you will learn the powerful classical mathematical techniques for efficient data analysis.
• Computational Methods. Here you will learn how modern computational techniques can be used to implement the relevant statistical methodology.
• Bayesian Statistics. Here you will learn how to use the Bayesian approach to statistics.

Learning Objectives
After successfully completing this course you should be able to:
• Understand of the main concepts of mathematical statistics, and use this understanding to solve a range of practical and theoretical problems in statistics.
• Recognise the role of Monte Carlo methods in modern statistics, and apply Monte Carlo techniques to simple problems.
• Apply the Bayesian approach to statistical inference, and understand its significance.

Class Contact
3 Lecture hours, 1 Tutorial hour

Assessment Summary
Problem Set(s): 40%
Final Exam: 60%

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.