After the course the student masters the basic principles of spatial statistics and is able to use R-packages (gstat and spatstat) to carry out statistical inference including interpolation, regression and model fitting for spatial data. In particular, the student is able to:
- design an optimal sampling scheme,
- distinguish between design-based and model-based sampling,
- estimate and interpret semi-variograms,
- carry out kriging interpolation with and without co-variables,
- validate kriging and spatial regression models,
- estimate the first and second order moment measures of a point process and interpret them,
- assess stationarity and isotropy,
- calculate elementary characteristics of Poisson and binomial point processes,
- simulate finite point processes,
- test for complete spatial randomness,
- estimate model parameters by maximum likelihood or maximum pseudo-likelihood,
- validate fitted point process models.
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Spatial data may come in various forms. Geostatistical data consist of a list of random measurements taken at fixed locations. In point pattern data the locations themselves are random. Examples of the former include weather and air quality data collected at monitoring stations. Optimal sampling is an important issue. Examples of point patterns include catalogues of the epicentres and magnitudes of earthquakes.
Specific topics that will be addressed include:
- spatial data handling in R
- spatial sampling theory
- geostatistical modeling and interpolation
- point process modeling
- statistical inference for Poisson processes
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