unbiasedKrige {intamap}

Unbiased kriging

Description

unbiasedKrige is a function for modifying a kriging prediction to a prediction that can be assumed to be unbiased for a certain threshold.

Usage

unbiasedKrige(object, formulaString, observations, predictionLocations,
              model, outputWhat, yamamoto, iwqmaxit = 500,
              iwqCpAddLim = 0.0001, debug.level, ...)

Arguments

object

either an object of the intamap type (see intamap-package for further description of the necessary content of this variable) or the output from the function krige in gstat. If the object is a result from the intamap procedure spatialPredict, the remaining arguments are not necessary.

formulaString

formula that defines the dependent variable as a linear model of independent variables; suppose the dependent variable has name z, for ordinary and simple kriging use the formula z~1; for universal kriging, suppose z is linearly dependent on x and y, use the formula z~x+y

observations

a Spatial*DataFrame with observations; should contain the dependent variable, independent variables, and coordinates

predictionLocations

the predictionLocations, only necessary if the method is "IWQSEL" and formulaString contains independent variables. Should preferentally be a grid if the method is "IWQSEL"

model

variogram model of dependent variable (or its residuals), defined by a call to vgm or autofitVariogram

outputWhat

Argument with type of unbiasedness method ("MOK" or "IWQSEL") and the thresholds.

yamamoto

logical describing if the yamamoto approach )is to be used in simulations. Defaults to yamamoto = FALSE when object is a Spatial*DataFrame.

iwqmaxit

maximum number of iterations in iwqsel

iwqCpAddLim

convergence criteria in iwqsel

debug.level

debug level, passed to subfunctions

...

other arguments that will be passed to subfunctions. These include

nsim

number of simulations necessary if the method is "IWQSEL". Defaults to nsim = 100 when object is a Spatial*DataFrame.

maxdist

maximum number of neighbours to use in local kriging, defaults to Inf

nmax

for local kriging: the number of nearest observations that should be used in simulations for the "IWQSEL" method in terms of the space of the spatial locations. Defaults to nmax = 10 when object is a Spatial*DataFrame.

Details

It is a fact that predictions from kriging tend to be biased towards the mean of the process. The function unbiasedKrige is a function that adds one or more predictions to the original output, which are assumed to be unbiased relative to a certain threshold. The two methods supported are the IWQSEL-method (Craigmile, 2006) and MOK (Skoien et al, 2008).

Value

an object of type intamap, as described in intamap-package, or a Spatial*DataFrame with one or more new prediction columns, representing different methods and thresholds.

Author(s)

Jon Olav Skoien

References

Craigmile, P. F., N. Cressie, T. J. Santner, and Y. Rao. 2006. A loss function approach to identifying environmental exceedances. Extremes, 8, 143-159.

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. Gecamin, Santiago, Chile, pp. 831-840.

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.

Examples

library(automap)
library(gstat)
data(meuse)
data(meuse.grid)
coordinates(meuse) = ~x+y
gridded(meuse.grid) = ~x+y

predictionLocations = meuse.grid[sample(1:length(meuse.grid),50),]
vmod = autofitVariogram(log(zinc)~1,meuse)$var_model
prediction = krige(log(zinc)~1,meuse,predictionLocations,vmod)
summary(prediction)

prediction <- unbiasedKrige(prediction,log(zinc)~1,
  meuse,  model = vmod, outputWhat = list(MOK = 6.0, MOK = 7.0, IWQSEL=7.0), 
  iwqmaxit = 100, iwqCpAddLim = 0.01)
summary(prediction)