intamap (version 1.4-9)

bayesCopula: Performs spatial interpolation using copulas

Description

Calculates predictive mean, predictive variance, predictive quantiles and exceedance probabilities for certain thresholds in the spatial copula model.

Usage

bayesCopula(obj,estimates,search=10,calc=list(mean=TRUE,variance=TRUE),testMean=FALSE)

Arguments

obj

Intamap object including observations and predictionLocations, see intamap-package

estimates

List of estimated parameters (typically obtained by calling copulaEstimation)

search

local prediction: number of observed locations considered for prediction at each unknown point

calc

list of what prediction type is required:

• mean = TRUETRUE if the predictive mean should be calculated, FALSE otherwise

• variance = TRUETRUE if the predictive variance should be calculated, FALSE otherwise

• quantiles = NULLVector of desired predictive quantiles, e.g. 0.95 or 0.05

• excprob = NULLVector of thresholds, where the probability of exceeding this threshold is desired

testMean

Whether or not the predictive means (if calculated) should be tested for being reasonable.

Value

List with the following elements:

mean

Mean of the predictive distribution. NULL if not calculated.

variance

Variance of the predtictive distribution. NULL if not calculated.

quantiles

Quantiles of the predictive distribution NULL if not calculated.

excprob

Probabilities for the predictive distribution to exceed predefined thresholds. NULL if not calculated.

Details

bayesCopula is used for plug-in prediction at unobserved spatial locations. The name of the function is somewhat misleading since no Bayesian approach is implemented so far. It is possible to calculate numerically the predictive mean and variance for both the Gaussian and the chi-square spatial copula model. Exceedance probabilities and predictive quantiles are only supported for the Gaussian copula model. Note that it may occur that the predictive distribution has no finite moments. In this case, a possible predictor is the median of the predictive distribution. If testMean=TRUE and the predictive means have no reasonable values, the median is automatically calculated and a warning is produced.

The copula prediction method is computationally demanding. There is a possibility of running it as a parallel process by setting the parameter nclus > 1 for the interpolation process. This requires a previous installation of the package doParallel.

References

[1] Kazianka, H. and Pilz, J. (2009), Spatial Interpolation Using Copula-Based Geostatistical Models. GeoENV2008 - Geostatistics for Environmental Application (P. Atkinson, C. Lloyd, eds.), Springer, New York

[2] 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.

See Also

copulaEstimation, spatialPredict, estimateParameters

Examples

# NOT RUN {
data(intamapExampleObject)
## estimate parameters for the copula model
copula <- list(method="norm")
anisotropy <- list(lower = c(0,1), upper = c(pi, Inf), params = c(pi/3, 2))
correlation <- list(model = "Ste", lower=c(0.01, 0.01, 0.01), upper = c(0.99, Inf, 20),
                    params = c(0.05, 4, 3))
margin <- list(name = "gev", lower = c(0.01, -Inf), upper = c(Inf, Inf), params = c(30, 0.5))
trend <- list(F = as.matrix(rep(1, 196)), lower = -Inf, upper = Inf, params = 40)
estimates <- copulaEstimation(intamapExampleObject, margin, trend, correlation, anisotropy, copula)
## make predictions at unobserved locations
predictions<-bayesCopula(intamapExampleObject, estimates, search = 25,
    calc = list(mean = TRUE, variance = TRUE, excprob = 40, quantile = 0.95))
# }