The potentials of geostatistics in predictive modelling

1
The potentials of geostatistics in predictive
modelling

• L.Hazelhoff
• ExploStat Consultancy Ltd.

2
Problem Objective

• What means spatial correlation for predictive
  modelling?
• What size of areas to predict mean value is
  reasonable?
• There is a lack of environmental data
• Objective To identify potentions of geostatiscs
  in predictive modelling

3
Overview presentation

• Introduction to geostatistics
• Exploratory analysis of spatial data
• Potentions for predictive modelling
• Demonstration of mapping sediments with the
  program Explostat (if there is time left)

1 km
4
Introduction to geostatistics

• Quantify spatial correlation with the variogram
• Interpolation and error estimation

5
Experimental Variogram(1)

• Define classes of distances between observations
• Select all pairs of observations from data set
  and classify their distances
• Square the difference of the measured values
  within each pair of observtions
• Add up these squares within a distance class
  (lag)
• Create a graph with distances on horizontal axis
  and mean semivariances on vertical axis

6
Experimental Variogram(2)
7
Experimental Variogram(3)
8
Fitting a Variogram
9
Interpolation with Kriging

• Define search area
• Minimum, maximal number of points
• Solve Kriging Equations to calculate weighing
  factors (depending on variogram)
• Calculate estimation error

Example of kriging equations in matrix notation
10
Exploratory Data analysis

• Stationairy mean and variance?
• Spatial Outliers?

How to deal with this conditions

• Use knowledge of environment physical parameters
  like type of soil, history of sedimentation and
  land use, geomorfological position in the
  landscape, hydrological situation, etc.

11
Inspection of the spatial data

• Visualization with Voronoi surface
• Link histogram and variogram with the spatial
  locations of observations
• Evaluate effect of removing outliers

12
Solutions for inhomogenious data distributions

• Stratification based on environmental knowledge
• Transformations with Principal Components
  (example for pollutions)

13
Example Stratification of spatial Data
14
Change of support

• Estimation at points Point kriging
• Estimation mean of an area Block kriging
• Error Point kriging gt Block kriging
• Error larger area lt error smaller area

15
Optimize Sampling Plan using Block Kriging

• Given Error Variance
• How many sampling locations?
• Optimal location of samples
• Iterative procedure

16
Interpolating more properties at the same time

• Co-Kriging with more variables
• Kriging of a derived variable using multivariate
  statistics. examples
• Principal Component score
• Factor Score
• Discriminant score
• Correspondence score
• Membership value (fuzzy classification)
• Etc.

17
Potentials for predictive modelling

• Generate optimal sampling plans (lack of
  sufficient environmental data)
• Optimal size of prediction area (balance between
  resolution of map and estimation error)
• Sampling cheap co-variables that are correlated
  with more expensive attributes (To reduce costs
  of fieldwork)

18
Conclusions

• There are potentials for using geostatistics in
  archeological predictive modelling
• Actual use of geostatistics have to be tested
• Collaboration between people with geostatistical
  expertise and people working in the field of
  predictive modelling should be usefull

19
THE END

• For more information about Explostat and
• download this presentation
• www.explostat.nl

Thank You