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covariance model: exponential

nugget     sill     range

     0 1.576983 0.7874607

REML

covariance model: gaussian

nugget     sill     range

     0 1.567491 0.7852996

summary(coalani.ml)

Parameters of the mean component (trend):

 beta

9.7224

Parameters of the spatial component:

  correlation function: powered.exponential

     (estimated) variance parameter sigmasq (partial sill) =  1.504

     (estimated) cor. fct. parameter phi (range parameter)  =  0.5439

     (fixed) extra parameter kappa =  0.5

  anisotropy parameters:

     (estimated) anisotropy angle = 0.6617  ( 38 degrees )

     (estimated) anisotropy ratio = 2.020

############################################################################

EXERCISE 4: PROFILE LIKELIHOOD

# profile log-likelihood for sill and range, here nugget is fixed

#first we give range of values to get the likelihood for sill -- range:

coal.ml<- likfit(coords=coal.m[,2:3],data=coal.m[,4], fix.nugget=T,

ini=c(.5,.5),

trend ="cte",method='ML',cov.model="exponential")

#now we get the profile likelihood:

coal.prof<-proflik(coal.ml,

coords=coal.m[,2:3],data=coal.m[,4],

sill.values=seq(0.1,5,length=5))

#this takes a couple of minutes

# to plot the  profile

plot.proflik(coal.prof)

###################################

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

PART II

Bayesian Spatial estimation and prediction:

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