Modelling zero-inflated spatially autocorrelated data with extreme values

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I have spatially explicit data (above; Longitude, Latitude) with measurements on a random variable (z). This data was not collected in a random or systematic fashion, but instead was recorded incidentally during other survey activities.


The data (see above; left hand figure is the raw data, right hand figure are log-transformed non-zero observations) is zero-inflated (approximately 90% of observations are zero), with a small number of extreme values thrown in for good measure.

I want to model this data in space so I can interpolate/predict values for the entire range of the data, but I am unsure what is my best approach. There appears to be so many options (e.g. geostatistics, GAMs, thin plate splines), but I am unsure where to start. R is my preferred analysis platform. Any suggestions would be greatly appreciated?



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