Description Usage Arguments Details Value Author(s) References Examples
ordinary kriging and simulation with an alternative kriging variance
1  yamamotoKrige(formula, Obs, newPoints, model, nsim = 0, nmax = 20, maxdist = Inf)

formula 
formula that defines the dependent variable as a linear model of
independent variables; suppose the dependent variable has name

Obs 

newPoints 

model 
variogram model  of the type that can be found by a call to

nsim 
integer; if set to a nonzero value, conditional simulation is used instead of kriging interpolation. For this, sequential Gaussian simulation is used, following a single random path through the data. 
nmax 
for local kriging: the number of nearest observations that should be used for a kriging prediction or simulation, where nearest is defined in terms of the space of the spatial locations. By default, all observations are used. 
maxdist 
maximum number of neighbours to use in local kriging, defaults to Inf 
The term yamamotoKrige
comes from the paper of Yamamoto (2000) where
he suggests using local variance around the kriging estimate (weighted with
the kriging weights) as an alternative kriging variance. This as a
solution to more reliable estimates of the kriging variance also when the
stationarity assumption has been violated. The method was applied by
Skoien et al. (2008), who showed that it can have advantages for cases where the
stationarity assumption behind kriging is violated.
If the number of observations is high, it is recommended have nmax
lower.
This is partly because the method relies on positive kriging weights. The method
to do this adds the norm of the largest negative weight to all weights, and rescales.
This tends to smooth the weights, giving a prediction closer to the average if a
too large number of observation locations is used.
Either a Spatial
*DataFrame with predictions and prediction variance,
in the columns var1.pred
and var1.var
, together with the
classical ordinary kriging variance in var1.ok
, or simulations with
column names simx
where x is the number of the simulation.
Jon Olav Skoien
Skoien, J. O., G. B. M. Heuvelink, and E. J. Pebesma. 2008. Unbiased block predictions and exceedance probabilities for environmental thresholds. In: J. Ortiz C. and X. Emery (eds). Proceedings of the eight international geostatistics congress. Santiago, Chile: Gecamin, pp. 831840.
Yamamoto, J. K. 2000. An alternative measure of the reliability of ordinary kriging estimates. Mathematical Geology, 32 (4), 489509.
Pebesma, E., Cornford, D., Dubois, G., Heuvelink, G.B.M., Hristopulos, D., Pilz, J., Stohlker, U., Morin, G., Skoien, J.O. INTAMAP: The design and implementation f an interoperable automated interpolation Web Service. Computers and Geosciences 37 (3), 2011.
1 2 3 4 5 6 7 8 9 10 11 12  library(gstat)
library(automap)
data(sic2004)
coordinates(sic.val) = ~x+y
coordinates(sic.test) = ~x+y
variogramModel = autofitVariogram(joker~1,sic.val)$var_model
newData = yamamotoKrige(joker~1,sic.val,sic.test,variogramModel,nmax = 20)
summary(newData)
plot(sqrt(var1.ok)~var1.pred,newData)
# Kriging variance the same in regions with extreme values
plot(sqrt(var1.var)~var1.pred,newData)
# Kriging standard deviation higher for high predictions (close to extreme values)

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