Approaches to Geo-mathematical Modelling

Chapter 21Research Priorities

Alan G. Wilson

In Chapter 1, we introduced the idea of a toolkit of methods for geo-mathematical modelling under the following headings:

• Estimating missing data: bi-proportional fitting and principal components analysis (Part 2)
• Dynamics in account-based models (Part 3)
• Space–time statistical analysis (Part 4)
• Real-time response models (Part 5)
• The mathematics of war (Part 6)
• Agent-based models (Part 7)
• Diffusion models (Part 8)
• Game theory (Part 9)
• Networks (Part 10).

Because the methods have been illustrated by examples of use, in almost all cases, combinations of tools are involved and there are more primitive underlying elements. For example, nearly every illustration involves some kind of spatial interaction modelling – a feature of the ‘geo’ focus of the book. The elements of the various systems of interest are usually ‘counted’, and we have shown how the formal construction of accounts is helpful and guarantees consistency. The use of the statistics toolkit is evidenced throughout. When we consider time – the dynamics – we formulate differential or difference equations in various ways. We show applications at different scales, and the micro scales in particular take us to the elements of the toolkit – notably, agent-based models and game theory. We have already noted the ubiquity of spatial interaction – the flows – and these flows are carried on networks, and hence the examples of Part 10. A characteristic of the field, shared by many ...