MATH3841 is a Mathematics Level III course. See the course overview below.

**Units of credit:** 6

**Prerequisites:** MATH3811 or MATH3911

**Exclusions:** MATH3820, MATH3870, MATH3920, MATH3941, MATH3970

**Cycle of offering:** Not offered each year.

**Graduate attributes: **The course will enhance your research, inquiry and analytical thinking abilities.

**More information:** This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH3841, you can log into UNSW Moodle for this course.

#### Course Overview

Measurements on different aspects of individual subjects are usually not independent, and to successfully describe the relationships between the various measurements, models for correlation or dependence are required. Similarly the successive observations on a time series, such as occur in financial application for example, will exhibit serial dependence and models which describe the serial dependence are useful for forecasting future values of the series. Spatially organised data, such as occur in environmental processes for example, similarly exhibit dependence between values observed at different sites.

The aim of this subject is to extend the student's understanding of statistical modelling, predominantly based upon independently distributed data, to these important practical examples where dependence is required in the models. The first half of the subject covers the multivariate normal distribution, and the marginal and conditional distributions derived from it as well as various important properties concerning optimal prediction. The multivariate normal distribution is central to the practicising statistician's understanding of dependence between measurements within subjects, across time or space.

The second half of the subject builds on the basic properties of the multivariate normal distribution by applying the results to a series of examples drawn from time series and spatial processes.

Students who complete this course can expect to have obtained a good understanding of the importance of modelling dependence in observed data as well as an understanding of the basic distributions and models useful in a range of practical situations.