# Senior Mathematics and Statistics Handbook

## Mathematical Statistics Units of Study

This chapter contains descriptions of units of study in the Mathematical Statistics program, arranged by semester.

## STAT3011 Stochastic Processes and Time Series

Prerequisite: STAT2011 or STAT2911 or STAT2001 or STAT2901, and MATH1003 or MATH1903 or MATH1907.

Prohibitions: STAT3911, STAT3003, STAT3903, STAT3005, STAT3905.

Lecturer: Ray Kawai .

Section I of this course will introduce the fundamental concepts of applied stochastic processes and Markov chains used in financial mathematics, mathematical statistics, applied mathematics and physics. Section II of the course establishes some methods of modeling and analysing situations which depend on time. Fitting ARMA models for certain time series are considered from both theoretical and practical points of view. Throughout the course we will use the S-PLUS (or R) statistical packages to give analyses and graphical displays.

There will be 3 lectures and 1 tutorial per week, and a total of 10 computer lab sessions in the semester.

Assessment: One two hour exam, assignments and quizzes (100%).

## STAT3911 Stochastic Processes and Time Series (Advanced)

Prerequisite: STAT2911 or credit in STAT2901, and MATH1003 or MATH1903 or MATH1907.

Prohibitions: STAT3011, STAT3003, STAT3903, STAT3005, STAT3905.

Lecturers: Qiying Wang .

This is an Advanced version of STAT3011. There will be 3 lectures in common with STAT3011. In addition to STAT3011 material, theory on branching processes and birth and death processes will be covered. There will be more advanced tutorial and assessment work associated with this unit.

There will be 3 lectures and 1 tutorial per week, plus an extra lecture on advanced material in the first half of the semester. There will be 7 computer lab sessions (on time series) in the second half of the semester.

Assessment: One two hour exam, assignments and quizzes (100%).

## STAT3012 Applied Linear Models

Prerequisite: STAT2012 or STAT2912 or STAT2004, and MATH1002 or MATH1902.

Prohibitions: STAT3002, STAT3004, STAT3902, STAT3904, STAT3912.

Lecturer: Emi Tanaka and Thomas Porter .

This course will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using classical linear methods, together with concepts of collection of data and design of experiments. First we will consider linear models and regression methods with diagnostics for checking appropriateness of models. We will look briefly at robust regression methods here. Then we will consider the design and analysis of experiments considering notions of replication, randomization and ideas of factorial designs. Throughout the course we will use the S-PLUS (or R) statistical packages to give analyses and graphical displays.

Assessment: One two hour exam, assignments and quizzes (100%).

## STAT3912 Applied Linear Models (Advanced)

Prerequisite: STAT2912 or credit in STAT2004, and MATH1902 or MATH2061 or MATH2961.

Prohibitions: STAT3002, STAT3004, STAT3902, STAT3904, STAT3012.

Lecturer: Thomas Porter .

This course will introduce the fundamental concepts of analysis of data from both observational studies and experimental designs using classical linear methods, together with concepts of collection of data and design of experiments. First we will consider linear models and regression methods with diagnostics for checking appropriateness of models. We will look briefly at robust regression methods here. Then we will consider the design and analysis of experiments considering notions of replication, randomization and ideas of factorial designs. Throughout the course we will use the S-PLUS (or R) statistical packages to give analyses and graphical displays.

There will be 3 lectures, 1 tutorial and 1 computer laboratory session per week.

Assessment: One two hour exam, assignments and quizzes (100%).

## STAT3013 Statistical Inference

Prerequisite: STAT2012 or STAT2912 or STAT2003 or STAT2903.

Prohibitions: STAT3001, STAT3901, STAT3913.

Lecturer: Shelton Peiris and Qiying Wang

Assessment: One 2 hour exam (70%), assignments, quizzes, computer practical reports.

In this course we will study basic topics in modern statistical inference. This will include traditional concepts of mathematical statistics: likelihood estimation, method of moments, properties of estimators, exponential families, decision-theory approach to hypothesis testing, likelihood ratio test, as well as more recent approaches such as Bayes estimation, Empirical Bayes and nonparametric estimation. During the weekly computer classes (using S-PLUS or R software packages) we will illustrate the various estimation techniques and give an introduction to computationally intensive methods like Monte Carlo, Gibbs sampling and EM-algorithm.

There will be 3 lectures, 1 tutorial and 1 computer laboratory session per week.

Prerequisite: STAT2912 or STAT2903.

Prohibitions: STAT3001, STAT3901, STAT3013.

Lecturer: Michael Stewart .

Assessment: One 2 hour exam (70%), assignments, quizzes, computer practical reports.

This unit is essentially an Advanced version of STAT3013, with emphasis on the mathematical techniques underlying statistical inference together with proofs based on distribution theory. There will be 3 lectures per week in common with some material required only in this advanced course and some advanced material given in a separate advanced tutorial together with more advanced assessment work.

There will be 3 lectures, 1 tutorial and 1 computer laboratory session per week.

## STAT3014 Applied Statistics

Prerequisite: STAT2012 or STAT2912 or STAT2004.

Assumed Knowledge: STAT3012 or STAT3912.

Prohibitions: STAT3914, STAT3006, STAT3002, STAT3902.

Lecturer: John Ormerod and Jean Yang .

Assessment: One two hour exam (70%), assignments and quizzes.

This unit has three distinct but related components: multivariate analysis, sampling and surveys, and generalized linear models. The first component deals with multivariate data covering simple data reduction techniques like principal components analysis and core multivariate tests including Hotelling’s T2, Mahalanobis’ distance, and Multivariate Analysis of Variance (MANOVA). The sampling section includes sampling without replacement, stratified sampling, ratio estimation, and cluster sampling. The final section looks at the analysis of categorical data via generalized linear models. Logistic regression and log-linear models will be looked at in some detail along with special techniques for analyzing discrete data with special structure.

There will be 3 lectures, 1 tutorial and 1 computer laboratory session per week.

Prerequisite: STAT2912 or Credit or better in STAT2004.

Assumed Knowledge: STAT3912.

Prohibitions: STAT3014, STAT3006, STAT3002, STAT3902, STAT3907.

Lecturer: John Ormerod .

Assessment: One two hour exam (60%), assignments and quizzes.

This unit is an Advanced version of STAT3014. There will be 3 lectures per week in common with STAT3014. The unit will have extra lectures focusing on multivariate distribution theory developing results for the multivariate normal, partial correlation, the Wishart distribution and Hotellling’s T2. There will also be more advanced tutorial and assessment work associated with this unit.

There will be 3 lectures, 1 tutorial and 1 computer laboratory session per week.