18th December 2015

- … and not
- GI Science
- Geography
- Spatial Statistics

- … for example?

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

*Needs* such as:

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

‘Classical’ spatial statistics:

- 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

- 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

- 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**

- this allows you to make Bayesian inferences about processes you can
- even if the likelihood is intractable

- 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**

- 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 \(d\)?