# Mathematics

## ECMM733 - Statistical Modelling in Space and Time (2018)

MODULE TITLE CREDIT VALUE Statistical Modelling in Space and Time 15 ECMM733 Prof Peter Challenor (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 0 0
 Number of Students Taking Module (anticipated) 12
DESCRIPTION - summary of the module content

Previous modules in statistics have treated data as independent and identically distributed, but real world data is not like that. In particular data collected in space and time can be highly correlated.  In this module you will look at methods of modelling such dependent data. Furthermore, you will examine how to model data as a field in n-dimensions, and the particular problems associated with time series.

AIMS - intentions of the module

In many applications of statistics data are referenced by space and time. Points that are close together are correlated so we cannot use methods that assume they are independent. In this module you will learn methods for modelling correlated data in one, two and higher dimensions as well as modelling time series. Although we will explain the theory in detail, we will concentrate on the real world, including examples from computer modelling, the environment and health.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module you should be able to:

Module Specific Skills and Knowledge:
1 model correlated data structures in continuous space and time co-ordinates;
2 explain what a Gaussian process is and how it can be used to model spatially correlated data in 1,2 or many dimensions;
3 describe the difference between space and time in modeling and create models using both ARIMA and state space modeling of time series;
4 demonstrate an understanding of spatio-temporal modeling;
5 use appropriate software and a suitable computer language for modelling correlated data in space, time and both together.
Discipline Specific Skills and Knowledge:
6 apply the theory of statistical modeling of spatially and temporally correlated data and analyse the resulting models.
Personal and Key Transferable / Employment Skills and Knowledge:
7 utilise advanced data analysis skills and be able to communicate associated reasoning and interpretations effectively in writing;
8 use relevant computer software competently;
9 utilise learning resources appropriately;

SYLLABUS PLAN - summary of the structure and academic content of the module

- dependent data; distance and correlation, stationarity, the Gaussian process; covariance functions; nuggets, sampling from Gaussian processes;

- types of covariance function, Bochner’s theorem; separability; fitting Gaussian processes; examples;

- kriging; variograms and covariance functions; time and space; ARIMA models; state space models; dynamic linear models;

- spatio-temporal models, hierarchical modelling.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study 33 115
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 22 Lectures Scheduled learning and teaching activities 11 Tutorials Guided independent learning 115 Coursework, background reading, preparation for contact time, preparation for assessments.

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Computer modelling and exercises 10 hours 1-2, 5-9 Written and oral

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams Practical Exams 20 80 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam (closed book) 80 2 hours - Summer Exam Period 1-7. 9 Oral (on request)
Coursework – computer modelling exercises and theoretical problems 1 10 10 hours 1-2, 5-9 Written and oral
Coursework – computer modelling exercises and theoretical problems 2 10 10 hours 1, 3-9 Written and oral

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
All above Written exam (closed book) 1-7,9 August Ref/Def period

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 50% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE: College to provide hyperlink to appropriate pages