Statistical Modelling in Space and Time - 2023 entry

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.

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.

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 modelling and create models using both ARIMA and state space modelling of time series;

4 Demonstrate an understanding of spatio-temporal modelling;

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.

- 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.

*Please refer to reassessment notes for details on deferral vs. Referral reassessment

ELE: http://vle.exeter.ac.uk

Reading list for this module: