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APTS module: Spatial and Longitudinal Data Analysis

This is a module which has been offered in the past but which is not currently available.

Module leader: P J Diggle

Please see the full Module Specifications PDF file document for background information relating to all of the APTS modules, including how to interpret the information below.

Aims: This module will introduce students to the statistical concepts and tools involved in modelling data which are correlated in time and/or space. The content will include models which are well established in statistical practice, although not usually well represented in the undergraduate curriculum, as well as examples of models which are central to current research in the area.

Learning outcomes: By the end of the module, students should have achieved:

  • a clear understanding of the meaning of temporal and spatial correlation;
  • a good working knowledge of standard models to describe both the systematic and the random parts of an appropriate model;
  • the ability to implement and interpret these models in standard applications;
  • an understanding of some of the key concepts which lie at the heart of current research in this area;
  • appreciation of at least one substantial case study.

Prerequisites: Preparation for this module should establish familiarity with:

  • standard models and tools for time series data, at the level of a typical undergraduate course on time series;
  • standard models and tools for spatial data at its simplest level;
  • inferential methods, including classical and Bayesian likelihood-based methods, to at least the level of the earlier APTS modules 'Statistical Inference' and 'Statistical Modelling'.

This module's preliminary web-lectures will cover the first two of the above pre-requisites.


  • Introduction: motivating examples; the fundamental problem — analysing dependent data.
  • Longitudinal data: linear Gaussian models; conditional and marginal models; why longitudinal and time series data are not the same thing.
  • Continuous spatial variation: stationary Gaussian processes; variogram estimation — what not to do and how to do it; likelihood-based estimation; spatial prediction.
  • Discrete spatial variation: Markov random field models.
  • Spatial point patterns: exploratory analysis; Cox processes and the link to continuous spatial variation; pairwise interaction processes and the link to discrete spatial variation.
  • Spatio-temporal modelling: spatial time series; spatio-temporal point processes.
  • Conclusion: review of available software (as preparation for mini-project); connections — spatial and longitudinal data analysis as two sides of the same coin.

Assessment: One of

  • A critique, in essay form, of a specified research paper, including both modelling and application aspects;
  • A mini-project involving the analysis of a data-set, selected by the student from several on offer (to allow students to focus on topics within the course which they find particularly interesting).