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Popular Methods in the Light of Modern Geostatistics 247

2
Figure 12.13. Data configuration in R . Measurements (hard data) are
available at points indicated by V; soft data are available at points
indicated by open circles. The estimation point is indicated by x.

and (ii.) the Gaussian model

both with a = 1. At three points that are kept fixed for all simulations
only (soft) interval data are provided. We assume that there are 13 inter-
vals [otj, otj+\}. The limits of these intervals are the threshold values that are
considered in IK. The intervals are defined as follows

1
where F x (p) is the p-quantile of the standard Gaussian law. Each point is
a
a
randomly assigned an interval x(Pi) e ( j> j+i]- Estimates Xk are sought
at the point p k—the same for all simulations. The ten points with known
process values constitute the hard data points, while the three locations with
interval data are the soft data points. In order to avoid methodological issues,
we assume that all parameters of the multivariate Gaussian law are known in
advance for both BME and IK. For the same reason, the same intervals have
been chosen for all points. BME does not require that the same intervals be
used for all points. Since we assume that complete knowledge about the dis-
tribution is available, we can use simple IK to compute the probabilities and