Establishing the Idea

Why Geocomputation ?

  • … and not
    • GI Science
    • Geography
    • Spatial Statistics
  • … for example?

Need more than ‘standard’ GIS:

“GIS was, for some, a backwards step because the data models and analysis methods provided were simply not rich enough in geographical concepts and understanding to meet their needs.”

http://www.geocomputation.org/what.html

Needs such as:

  • Fitting new (but more appropriate) models
  • Searching for spatial pattern
    • Visualisation
    • Knowledge discovery
    • Exploratory data analysis?

Fitting new models

Its not just about the models - its also about the approaches

‘Classical’ spatial statistics:
Assume \(y_i = X\beta + \epsilon\) where \(\epsilon = W\epsilon + \nu\) and \(\nu_i \sim N(0,\sigma^2)\)
  • But why? Were does this model come from?
  • Why is it linear?
  • Why does it depend on a specific set of spatial units? What about the MAUP?

“This lack of a well-defined link between process and form is commonplace in spatial analysis, and is well-documented in fields such as point set clustering and fractal analysis. That it also applies here, in spatial regression modeling, should come as no surprise.” De Smith, Goodchild, Longley 2007 - Geospatial Analysis: A Comprehensive Guide to Principles, Techniques and Software Tools P243

Process-oriented approaches

  • Some excellent ones exist
    • Cellular automata
    • Agent-based models
    • Microsimulation
  • All more grounded in reality
  • But some issues not fully addressed
    • Calibration
    • Model selection
    • Hypothesis testing
  • Maybe these are done better by classical approaches

A geocomputation solution?

  • Approximate Bayesian Computation (ABC)
  • See eg Marjoram, P., J. Molitor, V. Plagnol and S. Tavaré. Markov chain Monte Carlo without likelihoods. Proceedings of the National Academy of Sciences USA 100: 15324–15328.
  • Simplifying massively:
    • this allows you to make Bayesian inferences about processes you can simulate
  • even if the likelihood is intractable

A Quick overview

  • Draw parameter values from a prior distribution
  • Use these for the simulation
  • Keep them in a set of successful parameters if sufficiently ‘near’ to the real data
  • repeat these steps LOTS of times
  • the successful parameters have a distribution that should approximate the Bayesian posterior
  • Throw mud at the wall and see what sticks

Example - 2D hardcore point process

  • Random points but
    • Always separated by a distance \(d\)
  • Models
    • Locations of coins on fairground game
    • Locations of settlements?
    • Locations of animal nests?
  • Easy to simulate
  • Hard to manage analytically
  • How to estimate \(d\)?

ABC in Action…