A spatial random effect with one range for each region (the Difficult Terrain model component)

Haakon Bakka (NTNU, Trondheim, Norway)

Abstract:
Classical models in spatial statistics assume that the correlation between two points depends only on the distance between them (i.e. the models are stationary). In practice, however, the shortest distance may not be appropriate. Real life is not stationary! For example, when modelling fish near the shore, correlation should not take the shortest path going across land, but should travel along the shoreline. In ecology, animal movement depends on the terrain or the existence of animal corridors. We will show how this kind of information can be included in a spatial non-stationary model, by defining a different spatial range (distance) in each region.

We will answer the following questions:
- How to make a model with one range in each region?
- Is the algorithm fast enough for real data? (Hint: Yes)
- How to avoid overfitting with flexible random effects?
- How to interpret the inference when you have flexible random effects?
- How do we model a point process with different cluster sizes in different regions, without changing the average number of points?

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