# Statistics

### Statistics

**STAT2011 Statistical Models**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory week. Prerequisites: (MATH1001 or MATH1901 or MATH1906 or MATH1011) and (MATH1005 or MATH1905 or MATH1015 or STAT1021 or ECMT1010 or BUSS1020) Prohibitions: STAT2911, STAT2901, STAT2001 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

This unit provides an introduction to univariate techniques in data analysis and the most common statistical distributions that are used to model patterns of variability. Common discrete random models like the binomial, Poisson and geometric and continuous models including the normal and exponential will be studied. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The unit will have weekly computer classes where candidates will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method.

**STAT2012 Statistical Tests**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: MATH1005 or MATH1905 or MATH1015 or ECMT1010 or BUSS1020 Prohibitions: STAT2004, STAT2912 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

This unit provides an introduction to the standard methods of statistical analysis of data: Tests of hypotheses and confidence intervals, including t-tests, analysis of variance, regression - least squares and robust methods, power of tests, non-parametric tests, tests for count data, goodness of fit, contingency tables. Graphical methods and diagnostic methods are used throughout with all analyses discussed in the context of computation with real data using an interactive statistical package.

**STAT2911 Probability and Statistical Models (Adv)**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: (MATH1903 or MATH1907 or Credit in MATH1003) and (MATH1905 or MATH1904 or Credit in MATH1005 or Credit in ECMT1010 or Credit in BUSS1020) Prohibitions: STAT2011, STAT2001, STAT2901 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is essentially an advanced version of STAT2011, with an emphasis on the mathematical techniques used to manipulate random variables and probability models. Common distributions including the Poisson, normal, beta and gamma families as well as the bivariate normal are introduced. Moment generating functions and convolution methods are used to understand the behaviour of sums of random variables. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The notions of conditional expectation and prediction will be covered as will be distributions related to the normal: chi^2, t and F. The unit will have weekly computer classes where candidates will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method.

**STAT2912 Statistical Tests (Advanced)**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: MATH1905 or Credit in MATH1005 or Credit in ECMT1010 or Credit in BUSS1020 Prohibitions: STAT2004, STAT2012 Assumed knowledge: STAT2911 Assessment: One 2-hour exam, assignments and/or quizzes, computer practical reports and one computer practical exam (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is essentially an advanced version of STAT2012 with an emphasis on both methods and the mathematical derivation of these methods: Tests of hypotheses and confidence intervals, including t-tests, analysis of variance, regression - least squares and robust methods, power of tests, non-parametric methods, non-parametric smoothing, tests for count data, goodness of fit, contingency tables. Graphical methods and diagnostic methods are used throughout with all analyses discussed in the context of computation with real data using an interactive statistical package.

**STAT3011 Stochastic Processes and Time Series**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures and one 1 hour tutorial per week; ten 1 hour computer laboratories per semester. Prerequisites: (STAT2011 or STAT2911) and (MATH1003 or MATH1903 or MATH1907). Prohibitions: STAT3005, STAT3905, STAT3911, STAT3003, STAT3903 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

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.

**STAT3012 Applied Linear Models**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratories per week. Prerequisites: (STAT2012 or STAT2912) and (MATH1002 or MATH1014 or MATH1902) Prohibitions: STAT3902, STAT3904, STAT3004, STAT3912, STAT3002 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

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 R statistical package to give analyses and graphical displays.

**STAT3013 Statistical Inference**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: (STAT2011 or STAT2911) and (STAT2012 or STAT2912) Prohibitions: STAT3901, STAT3001, STAT3913 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

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 computer classes (using R software package) we will illustrate the various estimation techniques and give an introduction to computationally intensive methods like Monte Carlo, Gibbs sampling and EM-algorithm.

**STAT3014 Applied Statistics**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: STAT2012 or STAT2912 Prohibitions: STAT3914, STAT3002, STAT3902, STAT3006 Assumed knowledge: STAT3012 or STAT3912 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

This unit has three distinct but related components: Multivariate analysis; sampling and surveys; and generalised 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 T^2, 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.

**STAT3911 Stochastic Processes and Time Series Adv**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lecture, one 1 hour tutorial per week, plus an extra 1 hour lecture per week on advanced material in the first half of the semester. Seven 1 hour computer laboratories (on time series) in the second half of the semester (one 1 hour class per week). Prerequisites: (STAT2911 or credit in STAT2011) and (MATH1003 or MATH1903 or MATH1907) Prohibitions: STAT3003, STAT3005, STAT3011, STAT3905, STAT3903 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

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 Brownian bridges will be covered.

**STAT3912 Applied Linear Models (Advanced)**

Credit points: 6 Session: Semester 1 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: (STAT2912 or Credit in STAT2012) and (MATH2061 or MATH2961 or MATH1902) Prohibitions: STAT3904, STAT3004, STAT3012, STAT3002, STAT3902 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is essentially an Advanced version of STAT3012, with emphasis on the mathematical techniques underlying applied linear models together with proofs of distribution theory based on vector space methods. There will be 3 lectures per week in common with STAT3012 and some advanced material given in a separate advanced tutorial together with more advanced assessment work.

**STAT3913 Statistical Inference Advanced**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures, one 1 hour tutorial and one 1 hour computer laboratory per week. Prerequisites: STAT2911 and (STAT2012 or STAT2912) Prohibitions: STAT3901, STAT3001, STAT3013 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

This unit is 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.

**STAT3914 Applied Statistics Advanced**

Credit points: 6 Session: Semester 2 Classes: Three 1 hour lectures and one 1 hour computer laboratory per week plus an extra hour each week which will alternate between lectures and tutorials. Prerequisites: STAT2912 or credit or better in STAT2012. Prohibitions: STAT3902, STAT3907, STAT3002, STAT3014, STAT3006 Assumed knowledge: STAT3912 Assessment: One 2 hour exam, assignments and/or quizzes, and computer practical reports (100%) Mode of delivery: Normal (lecture/lab/tutorial) day

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 Hotelling's T^2. There will also be more advanced tutorial and assessment work associated with this unit.

**ENVX3002 Statistics in the Natural Sciences**

Credit points: 6 Teacher/Coordinator: Dr Thomas Bishop (Coordinator), Dr Floris Van Ogtrop (Coordinator). A/Prof Peter Thompson Session: Semester 1 Classes: 2x2 hr workshop/wk, 1x3 hr computer practical/wk Prerequisites: ENVX2001 or BIOM2001 or STAT2012 or STAT2912 or BIOL2022 or BIOL2922 Assessment: 1 Ã— Exam during the Exam period (50%), 5 Ã— Assessment Tasks (5x10%) Mode of delivery: Normal (lecture/lab/tutorial) day

This unit of study is designed to introduce students to the analysis of data they may face in their future careers, in particular data that are not well behaved, they may be non-normal, there may be missing observations or they may be correlated in space and time. In the first part, students will learn how to analyse and design experiments based on the general linear model. In the second part, they will learn about the generalisation of the general linear model to accommodate non-normal data with a particular emphasis on the binomial and poisson distributions, in addition to modelling non-linear relationships. In the third part linear mixed models will be introduced which provide the means to analyse datasets that do not meet the assumptions of independent and equal errors, for example data that is correlated in space and time. At the end of this unit, students will have learnt a range of advanced statistical methods and be equipped to apply this knowledge to analyse data that they may encounter in their future studies and careers.

Textbooks

Recommended readings: