Master of Statistics (MStat)

MS 1 In these regulations, and in the syllabuses for the degree of MStat, unless the context otherwise requires --

MS 2 To be eligible for admission to the courses leading to the degree of Master of Statistics a candidate

(a)

shall comply with the General Regulations;

(b)

shall hold

(i)	a Bachelor's degree with honours of this University; or
(ii)	another qualification of equivalent standard from this University or from another university or comparable institution accepted for this purpose; and

(c)

shall satisfy the examiners in a qualifying examination if required.

(a)	A qualifying examination may be set to test the candidate's formal academic ability or his ability to follow the courses of study prescribed. It shall consist of one or more written papers or their equivalent, and may include a project report.
(b)	A candidate who is required to satisfy the examiners in a qualifying examination shall not be permitted to register until he has satisfied the examiners in the examination.

MS 4 To be eligible for the award of the degree of Master of Statistics a candidate

(a)	shall comply with General Regulations; and
(b)	shall complete the curriculum and satisfy the examiners in accordance with the regulations set out below.

MS 5 The curriculum shall extend over not less than one academic year of full-time study, or not less than two and not more than three academic years of part-time study, with a minimum of 300 hours of prescribed work, and shall include an examination in courses to the value of 15 units, all to be held in the manner prescribed in the syllabuses.

(a)	shall follow courses of instruction and complete satisfactorily all prescribed written work and field work;
(b)	shall satisfy the examiners in the prescribed courses and in any prescribed form of examination; and
(c)	if appropriate, shall complete and present a satisfactory project paper in lieu of one written paper in the examination, if such option is provided in the syllabus.

(a)	Where so prescribed in the syllabuses, coursework or a project paper may constitute part or whole of the examination for one or more courses.
(b)	An assessment of the candidate's coursework during his studies, including completion of written assignments and participation in field work or laboratory work, as the case may be, will be taken into account in determining the candidate's result in each paper. Except where otherwise stated, the weight assigned to coursework will be 25% of the total marks.

MS 8 A candidate who has failed to satisfy the examiners at his first attempt in not more than half of the total number of units to be examined, whether by means of written examination papers, project paper and coursework assessment, during any of the academic years of study, may be permitted

(a)	to present himself either for re-examination in the course or courses of failure, with or without repeating any part of the curriculum, or for examination in the same number of new courses, except that courses designated as compulsory are not replaceable under this provision; or
(b)	to repeat a year of the curriculum and present himself for examination in the courses prescribed for the repeated year.

MS 9 Subject to the provisions of Regulation MS 6(c), a candidate who has failed to present a satisfactory project paper may be permitted to submit a new or revised project paper within a specified period.

MS 10 A candidate who has failed to satisfy the examiners in any prescribed field work or practical work may be permitted to present himself for re-examination in field work or practical work within a specified period.

MS 11 A candidate who is unable because of illness to be present for one or more papers in any written examination other than that held in his final academic year of study may apply for permission to present himself at a supplementary examination to be held before the beginning of the following academic year. Any such application shall be made on the form prescribed within two weeks of the first day of the candidate's absence from the examination.

(a)	is not permitted to present himself for re-examination in any written paper or any course examined by means of coursework assessment, or in field work or practical work in which he has failed to satisfy the examiners and is not permitted to repeat a year of the curriculum under the provisions of Regulation MS 8; or
(b)	has failed to satisfy the examiners in any written paper or any course examined by means of coursework assessment, or field work or practical work at a second attempt; or in any new course selected under the provision of MS 8(a); or
(c)	is not permitted to submit a new or revised project paper under the provisions of Regulation MS 9; or
(d)	has failed to submit a satisfactory new or revised project paper under the provisions of Regulation MS 9

may be required to discontinue his studies under the provisions of General Regulation G 12.

MS 13 At the conclusion of the examination, and after presentation of the project paper if applicable, a pass list shall be published in alphabetical order. A candidate who has shown exceptional merit at the whole examination may be awarded a mark of distinction, and this mark shall be recorded in the candidate's degree diploma.

The curriculum shall extend over not less than one academic year of full-time study, or not less than two and not more than three academic years of part-time study, with a minimum of 300 hours of prescribed work.

Courses selected from the following list and totalling 15 units will be prescribed by the Department. The Department will consider the student's wishes in course prescription, but will also take into account the details of the student's undergraduate training, to avoid overlaps.

Where applicable, the weights assigned to performance in the examination and an assessment of coursework in evaluating a candidate's final grade in each course will be in the ratio 75:25.

17901.    Distribution theory
17902.    Computationally-intensive methods in statistics
17903.    Advanced models in time series
17904.    Measure theory and probability
17905.    Asymptotic methods in probability and statistics
17906.    Spatial statistics and stereology
17907.    Topics in stochastic processes
17908.    Project
17909.    Reading course (A)

17910.    Multivariate statistical analysis
17911.    Time series
17912.    Applied probability modelling
17913.    Selected topics in statistics
17914.    Case studies in statistical consulting
17915.    Applications of statistics
17916.    Advanced theory of inference
17917.    Reading course (B)

This course on probability distributions reviews the standard results often, but not always, covered in undergraduate courses and provides an introduction to many new distributions and techniques for their manipulation. Review material includes: the characteristic function, cumulants, transformation of random variables, mixtures, the multivariate normal and its quadratic forms. The course proceeds with a comprehensive overview of the standard (and not-so-standard) distributions, focusing on their genesis and inter-relationship. Other topics include: Order statistics, including distribution of the median and range; non-central distributions associated with normal theory; non-normal multivariate distributions.

Certain statistical methods rely heavily on intensive computations. These methods include: simulation, statistics based on permutation considerations, 'jackknife' statistics and 'bootstrap' techniques. With the advent of modern computers, exposure to these techniques is necessary for a statistician. A project paper may be used in place of all or part of the written examination.

Advanced topics in time-series analysis will be chosen from the following areas: introduction to further nonlinear models; conditional heteroskedastic and related models; threshold models; bilinear models; chaos. Ergodicity; stationarity and invertibility properties in nonlinear time-series. Time-series model estimation and hypothesis testing. Topics in multiple time-series analysis. Problems in nonstationary time-series modelling; unit root tests; cointegration models and error correction models. A project paper may be used in place of all or part of the written examination.

Many research fields in both probability and statistics depend upon the abstract language of probability measure-spaces and on the general integration theory that arises in this setting. This course provides the necessary background for potential research students and for those wishing to read the large literature which depends on this theory. Topics include: set and measure theory; probability spaces; extension of measures; random variables as measurable functions; convergence of sequences of random variables; different modes of convergence; strong law of large numbers; the general integral; monotone and bounded convergence theorem; Fubini theorem; convergence of measures.

Often one finds that a desired result, such as an expression for a distribution function or for the probability of an event, is very complicated (or even unavailable). In many cases, the result takes a simple form as one (or more) of the quantities in the problem tend to infinity. These forms can provide excellent approximations for the finite case. This course deals with these asymptotic methods. The most common application in statistics is when sample size is the asymptotic quantity. Topics include: limiting distributions; use of limiting characteristic functions; central limit theorems; Slutzky's theorem; poisson limit laws for sums of dependent binary variables; asymptotics of U-statistics; extreme value theory, coverage problems.

This course deals with the statistics of spatial patterns, focussing on 'stereology', the science of drawing inferences from data collected in a lower dimension (e.g. from the projection of or sectioning of a 3-d object). Spatial statistics: analysis of spatial point processes; models for point processes and processes of other geometric objects. Geometry: the basic geometry and topology of objects in 1, 2 and 3 dimensions. Stereology: the information contained in lower-dimensional sections and probes of spatial structures; estimation of the number and geometric properties (such as volume and surface area) of objects from the information on sections; applications to medical and biological research, geography, geology, and mining. A project paper may be used in place of all or part of the written examination.

An advanced course on topics such as: the Wiener process; stochastic integration with applications in finance; martingales; optimal stopping times; random fields; point processes; random set processes.

A project in any branch of statistics or probability will be chosen, through consultation between students and lecturers. A substantial written report is required. This must be submitted by July 31 of the academic year.

This course consists of supervised reading and written work. A candidate will specialize in one topic under the guidance of a lecturer. Topics vary yearly depending on the current interests of staff. A written report is required in lieu of a written examination paper. It must be completed and submitted by January 31 of the academic year.

In many disciplines the basic data on an experimental unit consist of a vector of possibly correlated measurements. Examples include the chemical composition of a rock, the results of clinical observations and tests on a patient, the household expenditures on different commodities. Through the challenge of problems in a number of fields of application, this course considers appropriate statistical models for explaining the patterns of variability of such multivariate data. Topics include: multiple, partial and canonical correlation; multivariate regression; tests on means and covariances; multivariate ANOVA; principal components analysis; factor analysis; covariance analysis for structural linear equation models; discriminant analysis and classification; cluster analysis; multidimensional scaling; correspondence analysis. Assessment: 40% coursework, 60% examination.

A time series consists of a set of observations on a random variable taken over time. Such series arise naturally in climatology, economics, environmental research and many other disciplines. In addition to statistical modelling, the course deals with the prediction of future behaviour of these time series. This course distinguishes different types of time series, investigates various linear or non-linear representations for them and studies the relative merits of different forecasting procedures. Assessment: 40% coursework, 60% examination.

This course builds on the basic techniques of probability theory established in a standard first course on random processes, expanding the domain of application to diverse areas and developing new techniques for problem solving. Contents vary according to staff interests but may include: further theory of Markov processes; age-dependent and multitype branching processes with application to population dynamics and biological cell colonies; stochastic models in road traffic; applications of point processes; Markov random fields; stochastic reversibility; interacting particle systems; models of epidemics; queueing theory.

This course comprises nine modules. Modules that may be included are: clinical trials; sequential methods; martingale estimating equations; compositional data; U-statistics; robust methods; E-M algorithm; survival analysis; relative-risk regression models; log-linear models; directional data methods.

Staff in the department will present to the students in this course their own consulting experience. Statistical consulting, drawn from research papers and books, will also be presented as case studies. A project paper may be used in place of all or part of the written examination.

This course will demonstrate how statistics can be applied in various application areas. When discussing a particular application area, the focus will be on the problems and statistical practices of that area. This contrasts with the style in our other courses, where our focus is on particular methodologies and their application. Application areas that may be included in this course are: biostatistics; econometrics; environmental statistics; statistics in the law; geostatistics; statistics in medical research. A project paper may be used in place of all or part of the written examination.

This course will cover the advanced theory of point estimation, interval estimation and hypothesis testing. Topics on estimation theory are: group families; exponential families; sufficient statistics and minimal sufficiency; ancillary statistics; complete statistics; UMVU estimators; information inequality (multiparameter case); convex loss functions; Bayes estimation; minimax estimation; admissibility; shrinkage estimators: large-sample MLE theory. Topics on hypothesis testing include: uniformly most powerful tests, monotone likelihood ratio; unbiasedness for hypothesis testing; similarity and completeness; UMP unbiased tests for multiparameter exponential families; confidence intervals and families of tests; unbiased confidence sets; maximal invariants; most powerful invariant tests; large -sample likelihood-ratio theory.

This course is similar in character to course 17909. Reading course (A), but the amount of reading and writing work is doubled. The written report(s) have a May 31 deadline.

1 unit courses (except course 17908 and 17909) shall be examined by one two-hour written paper. 2 unit courses (except course 17917) shall be examined by one three-hour written paper.