SpatialTools (version 0.5.8)

krige.ok: Performs Ordinary Kriging

Description

Performs Ordinary Kriging using y, the $n \times 1$ matrix of observed responses, V, the (positive definite) covariance matrix of the observed responses, Vp, the $np \times np$ covariance matrix of the responses to be predicted, and Vop, the $n \times np$ matrix of covariances between the observed responses and the responses to be predicted.

Usage

krige.ok(y, V, Vp, Vop, ...)

Arguments

y

The vector of observed responses. Should be a matrix of size $n \times 1$ or a vector of length $n$.

V

The covariance matrix of the observed responses. The size is $n \times n$.

Vp

The covariance matrix of the responses to be predicted. The size is $np \times np$.

Vop

The cross-covariance between the observed responses and the responses to be predicted. The size is $n \times np$

...

Several additional arguments may be supplied. If user specifies nsim to be a positive integer, then nsim conditional realizations of the predictive distribution will be generated. If this is less than 1, then no conditional sim

Value

• The function a list containing the following objects:
• pred
  A vector of length $np$ containing the predicted responses.
• mspe
  A vector of length $np$ containing the mean-square prediction error of the predicted responses.
• coeff
  A vector of length $k$ containing the estimated regression coefficients.
• vcov.coeff
  A $k \times k$ matrix containing the (estimated) covariance matrix of estimated the regression coefficients.
• simulations
  An $n \times nsim$ matrix containing the nsim realizations of the conditional realizations. Each column of the matrix represents a realization of the conditional normal distribution.

Details

It is assumed that there are $n$ observed data values and that we wish to make predictions at $np$ locations.

References

Statistical Methods for Spatial Data Analysis, Schabenberger and Gotway (2003). See p. 226-228.

Examples

# create observed and predicted coordinates
ocoords <- matrix(runif(100), ncol = 2)
pcoords <- matrix(runif(200), ncol = 2)

# include some observed locations in the predicted coordinates
acoords <- rbind(ocoords, pcoords)

# create covariance matrix
C3 <- cov.sp(coords = ocoords, sp.type = "matern", sp.par = c(2, 1), smoothness = 1, 
	finescale = 0, error = 0.5, pcoords = acoords)

# generate data with error
y <- rmvnorm(nsim = 1, mu = rep(2, 50), V = C3$V) + rnorm(50, sd = sqrt(.5))

# use universal kriging to make predictions.  Do not do conditional simulation
krige.obj <- krige.ok(as.vector(y), V = C3$V, Vp = C3$Vp, Vop = C3$Vop, 
	nsim = 0)

#Do conditional simulation
krige.obj2 <- krige.ok(as.vector(y), V = C3$V, Vp = C3$Vp, Vop = C3$Vop, 
	nsim = 100, Ve.diag = rep(.5, 50), method = "eigen")