GeoScores function

Computation of predictive scores

The function computes some predictive scores for a spatial, spatiotemporal and bivariate Gaussian RFs UTF-8

GeoScores(data_to_pred, probject=NULL,pred=NULL,mse=NULL,
   score=c("brie","crps","lscore","pit","pe"))

Arguments

• data_to_pred: A numeric vector of data to predict about a response
• probject: A Geokrig object obtained using the function Geokrig
• pred: A numeric vector with predictions for the response.
• mse: a numeric vector with prediction variances.
• score: A character defining what statistic of the prediction errors should be computed. Possible values are lscore, crps, brie and pe. In the latter case scores based on prediction errors such as rmse, mae, mad are computed. Finally, the character pit allows to compute the probability integral transform for each value

Details

GeoScores computes the items required to evaluate the diagnostic criteria proposed by Gneiting et al. (2007) for assessing the calibration and the sharpness of probabilistic predictions of (cross-) validation data. To this aim, GeoScores uses the assumption that the prediction errors are Gaussian with zero mean and standard deviations equal to the Kriging standard errors. This assumption is an approximation if the errors are not Gaussian.

Returns

Returns a list containing the following informations: - LSCORE: Logarithmic predictive score

• CRPS: Continuous ranked probability predictive score

• RMSE: Root mean squared error

• MAE: Mean absolute error

• MAD: Median absolute error

• PIT: A vector of probability integral transformation

References

Gneiting T. and Raftery A. Strictly Proper Scoring Rules, Prediction, and Estimation. Journal of the American Statistical Association, 102

Author(s)

Moreno Bevilacqua, moreno.bevilacqua89@gmail.com ,https://sites.google.com/view/moreno-bevilacqua/home, Víctor Morales Oñate, victor.morales@uv.cl , https://sites.google.com/site/moralesonatevictor/, Christian", Caamaño-Carrillo, chcaaman@ubiobio.cl ,https://www.researchgate.net/profile/Christian-Caamano

Examples

library(GeoModels)

################################################################
######### Examples of predictive score computation  ############
################################################################

library(GeoModels)
model="Gaussian"
set.seed(79)
N=1000
x = runif(N, 0, 1)
y = runif(N, 0, 1)
coords=cbind(x,y)

# Set the exponential cov parameters:
corrmodel = "GenWend"
mean=0; sill=5; nugget=0
scale=0.2;smooth=0;power2=4

param=list(mean=mean,sill=sill,nugget=nugget,scale=scale,smooth=smooth,power2=power2)

# Simulation of the spatial Gaussian random field:
data = GeoSim(coordx=coords, corrmodel=corrmodel,
              param=param)$data

sel=sample(1:N,N*0.8)
coords_est=coords[sel,]; coords_to_pred=coords[-sel,]
data_est=data[sel]; data_to_pred=data[-sel]

## estimation with pairwise likelihood
fixed=list(nugget=nugget,smooth=0,power2=power2)
start=list(mean=0,scale=scale,sill=1)
I=Inf
lower=list(mean=-I,scale=0,sill=0)
upper=list(mean= I,scale=I,sill=I)
# Maximum pairwise likelihood fitting :
fit = GeoFit(data_est, coordx=coords_est, corrmodel=corrmodel,model=model,
                    likelihood='Marginal', type='Pairwise',neighb=3,
                    optimizer="nlminb", lower=lower,upper=upper,
                    start=start,fixed=fixed)
# locations to predict
xx=seq(0,1,0.03)
loc_to_pred=as.matrix(expand.grid(xx,xx))

pr=GeoKrig(loc=coords_to_pred,coordx=coords_est,corrmodel=corrmodel,
       model=model,param= param, data=data_est,mse=TRUE)

Pr_scores =GeoScores(data_to_pred,pred=pr$pred,mse=pr$mse)
Pr_scores$rmse;Pr_scores$brie
hist(Pr_scores$pit,freq=FALSE)