18  Challenges of geostatistical methods


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18.1 Geostatistical data analysis today

Spatial data analysis - examples

Binary responses – Landslide occurrence

Data used in computer practical of chapter 24.

European wide air pollution mapping

Feature engineering - algorithms

Feature engineering - settings

These are now just derivatives from one data set (elevation model). We could also have different datasets, and not be sure which is best to include. An example is meteorological data, where often different versions exist (e.g. average yearly rainfall over different periods, computed by different models or based on a different set of rainfall stations).

Multi-attribute soil mapping

18.2 Challenges for classical geostatistics


  1. What “properties” does a spatial prediction method need to have to handle today’s spatial data problems?


  1. What are the challenges with classical geostatistical approaches regarding these “properties”?


Answers

Today’s requirements for a method

Deal with …

  • large number of responses,

  • responses of any data type (binary, nominal, ordered, continuous),

  • non-Gaussian continuous responses,

  • large numbers of covariates,

  • increasing number of data points,

  • mapping for huge surfaces for many prediction nodes (e.g. high-resolution global mapping),

  • non-Gaussian uncertainty distributions of predictions.

We need …

  • automatic selection of relevant covariates,

  • automatic building of model structure,

  • relaxed model assumptions regarding residual distribution,

  • good performance to fit the model with large numbers of observations,

  • good performance to predict for large numbers of nodes,

  • non-parametric uncertainty quantification.

Problems with kriging approaches

  • Assumption on Gaussian residual distribution and stationarity

  • Manual modelling steps like residual analysis

  • Model selection for trend very challenging for large number of covariates

  • Very sensitive to multi-collinear covariates

  • Slow model fitting for large number of points

  • Slow prediction for large number of prediction locations