GeoScores: Computation of predictive scores

In GeoModels: Procedures for Gaussian and Non Gaussian Geostatistical (Large) Data Analysis

Computation of predictive scores

Description

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

Usage

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.

Value

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

Author(s)

Moreno Bevilacqua, [e-mail],https://sites.google.com/view/moreno-bevilacqua/home, Víctor Morales Oñate, [e-mail], https://sites.google.com/site/moralesonatevictor/, Christian", Caamaño-Carrillo, [e-mail],https://www.researchgate.net/profile/Christian-Caamano

References

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

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)

GeoModels documentation built on April 13, 2025, 5:09 p.m.