Module
Blurbs
ST1131 Introduction to Statistics
Statistics is a vital skill in the repertoire of scientists, engineers and social scientists. This module will introduce you to the fundamental concepts and methodologies of statistics. You will learn how to summarise complex data, the basic concepts of probability, statistical estimation and how to test hypotheses. All the methods will be illustrated via interesting data and you will learn how to perform the analyses quickly and painlessly on a computer.
ST2132 Mathematical Statistics
This module lays the mathematical framework for all the advanced topics in statistics. It introduces the critical concept of the likelihood function, which underpins all of statistics. For instance, classical parameter estimation is performed by maximising the likelihood function over the parameters of the model, and uncertainty in those estimates can be characterised via confidence intervals derived from the Fisher information, which in turn comes from the likelihood function. The mathematical foundation for hypothesis testing and some of the common distributions will be covered.
This module is vital to those students wishing to major in statistics.
ST2137 Computer Aided Data Analysis
Almost all modern statistical analysis is carried out on a computer. This module will teach you how to use common statistical packages such as SAS, R and SPSS---chosen due to their tremendous popularity in industry---to analyse data. You will learn how to access and manipulate data structures, implement the tests you learned in other modules (such as analysis of variance), generate pseudorandom numbers and perform resampling methods and simulations. The skills you learn on this course will be particularly valuable in the rest of your studies.
ST3131 Regression Analysis
Regression is one of the principle tools in the modern statistician's toolkit. It involves using one or more variables to predict or explain a response. Examples throughout science, medicine, engineering and the social sciences abound; here are a few:
• using distance from imprisoned populations of jellyfish to a postulated ancestral source to predict genetic diversity;
• using floor area, age, level and location of an apartment to predict the value of the apartment;
• using genetic expression of other genes in a gene sequence to explain the expression of cellulose synthase producing genes.
This course will take you beyond the simple linear regression that you may already be familiar with (one predictor explaining one response) and into the realms of multiple predictors, not all of which may be good predictors, and some of which may interact with each other in complex ways. Along the way you will learn the art of model building and the science of model diagnostics. You will see how some basic statistical techniques with which you are already familiar---such as t-tests and analyses of variance---can be recast within the multiple regression framework.
This course is one of the pre-requisites for the 4th level module, ST4233 Linear Models, so if you wish to take that module in the future, you should think about taking this module now.
ST3233 Applied Time Series Analysis
Time series are perhaps one of the most familiar forms of data from our everyday lives. They take the form of observations that are linked over or indexed by time. Examples include:
• the daily movements of a stock index;
• temperature fluctuations at a weather recording station over a time course of days to years;
• annual counts of an endangered wild marsupial population;
• the monthly sales figures of a merchandise.
This linking of observations in time means that observations cannot be considered to be an independent random sample as in many other applications of statistics. Instead this dependency structure must be accounted for. One way to do this is via a family of models called ARIMA---auto-regressive (i.e. regressing upon itself) integrated moving averages. This course will focus on ARIMA models, and you will learn what exactly an ARIMA model is, how to estimate their parameters, and how to perform predictions of the future evolution of the time series using the fitted ARIMA model.
ST3234 Actuarial Statistics
The actuarial industry is one of the major employers of professional statisticians globally. Actuarial statistics involves quantifying the risk of adverse events---such a death or serious illness---so that a fair price can be set for insurance (and pensions) to offset that risk for consumers.
This module will teach you many of the practical issues involved in the actuarial profession, including the distribution of life remaining via survival models and life tables, how this relates to the cost of pensions or life insurance via annuities, assurances and premiums, and the concepts of collective risk theory and minimal reserves.
This module is particularly valuable to those students considering a career as an actuary or in finance.
ST3236 Stochastic Processes 1
A stochastic process is any process in which randomness at one point in time (or space) has a knock-on effect on the process at another time (or location). Examples of stochastic processes include:
• traffic: in which a small delay in bus arrival leads to more passengers awaiting the bus at the next stop, requiring more time for the bus to catch up with those passengers, leading to a greater delay at the next stop and so on (this is the mechanism leading to the oft-remarked upon phenomenon of buses arriving in twos or threes);
• the propagation of evolutionary fit genes: those genes that lead to greater reproductive fitness are more likely to be taken forward to the next generation, but if starting from a low initial frequency, even highly fit genes are at risk of dying out early in their invasion.
A great many other real-world phenomena can be modelled as stochastic processes, and indeed modern statistical computing makes great use of stochastic processes in fitting models via Markov chain Monte Carlo.
In this module you will learn the theory underpinning stochastic processes. The course will focus on discrete time models, which are appropriate for many scenarios. The course is a prerequisite for ST4238 Stochastic Processes 2, so if you wish to take that module, you should take this one first.
ST4231 Computer Intensive Statistical Methods
Modern applied statistics is heavily dependent on computational techniques. A great many applied problems simply cannot be tackled by theory alone, but require a computationally intensive approach to reach a solution. This course will introduce you to some of the more popular and commonly exploited computational, statistical techniques. These include
• the bootstrap method for forming confidence intervals when analytic confidence intervals are unobtainable;
• the expectation-maximisation algorithm for dealing with the otherwise potential biasing problem of missing data; and
• Markov chain Monte Carlo methods for evaluating difficult integrals: an extremely popular methodology within the Bayesian philosophical paradigm.
The skills you learn in this module will be particularly useful to you if you undertake any statistical research in the future, such as an honour's year project.
ST4232 Nonparametric statistics
Most of the statistical techniques you have learned this fair in your studies depend on the assumption of normal errors. This is called a parametric assumption, because the data are assumed (often without testing) to come from a specified family of distributions. Nonparametric statistics, on the other hand, does not require such distributional assumptions, and therefore benefits from increased robustness, because conclusions drawn are valid even if the data do not follow the postulated distribution.
In this module you will learn how to adapt many of the techniques you have already learned to the more robust, nonparametric setting.
ST4233 Linear Models
This course builds upon the module on regression analysis that is a prerequisite for the course. A variety of advanced topics in regression are covered, ranging from general linear models to generalised linear models.
ST4241 Design and Analysis of Clinical Trials
The pharmaceutical industry is one of the major employers of statisticians. Statistics plays an important role in all stages of the development of a new drug, from dosage trials in healthy volunteers through to efficacy trials in the target population. This module will introduce you to the statistical techniques needed to design and analyse such clinical trials, alongside some of the ethical issues that arise in dealing with what can be life and death decisions.
