https://github.com/cran/RandomFields
Tip revision: b56f7a28e59b21773db3483310cae6fa56c716eb authored by Martin Schlather on 26 April 2016, 01:33:08 UTC
version 3.1.12
version 3.1.12
Tip revision: b56f7a2
RFloglikelihood.Rd
\name{RFloglikelihood}
\alias{RFloglikelihood}
\alias{RFlikelihood}
\title{Likelihood and estimation of linear models}
\description{
\command{\link{RFloglikelihood}} returns the log likelihood for Gaussian
random fields. In case NAs are given that refer to linear modeling, the
ML of the linear model is returned.
}
\usage{
RFlikelihood(model, x, y = NULL, z = NULL, T = NULL, grid = NULL,
data, distances, dim, likelihood,
estimate_variance =NA, ...)
}
\arguments{
\item{model}{object of class \code{\link[=RMmodel-class]{RMmodel}};
the covariance or variogram model, which is to be evaluated}
\item{x}{vector or \eqn{(n \times \code{dim})}{(n x
\code{dim})}-matrix, where \eqn{n} is the number of points at
which the covariance function is to be evaluated;
in particular,
if the model is isotropic or \code{dim=1} then \code{x}
is a vector. \code{x}}
\item{y}{second vector or matrix for non-stationary covariance
functions}
\item{z}{z-component of point if xyzT-specification of points is used}
\item{T}{T-component of point if xyzT-specification of points is used}
\item{grid}{boolean; whether xyzT specify a grid}
\item{data}{vector or matrix of values measured at \code{coord};
If a matrix is given then the columns are interpreted as independent
realisations.\cr
If also a time component is given, then in the data the indices for
the spatial components run the fastest.
If an \code{m}-variate model is used, then each realisation is given as
\code{m} consecutive columns of \code{data}.
}
\item{distances}{vector;
the lower triangular part of the distance matrix column-wise;
equivalently the upper triangular part of the distance matrix row-wise;
either \code{x} or \code{distances} must be missing}
\item{dim}{dimension of the coordinate space in which the model is
applied; only necesary for given \code{distances}}
\item{likelihood}{ not programmed yet. Character.
choice of kind of likehood ("full", "composite", etc.),
see also \code{likelihood} for \command{\link{RFfit}}
in \command{\link{RFoptions}}.
}
%\item{log}{logical. If \code{TRUE} the loglikelihood is returned.
% }
\item{estimate_variance}{logical or \code{NA}. See Details.
}
\item{...}{for advanced
further options and control arguments for the simulation
that are passed to and processed by \command{\link{RFoptions}}
}
}
\details{
The function calculates the likelihood for data of a Gassian process
with given covariance structure.
The covariance structure may not have \code{NA} values in the
parameters except for a global variance. In this case the variance
is returned that maximizes the likelihood.
Additional to the covariance structure the model may include a
trend. The latter may contain unknown linear parameters.
In this case again, the unknown parameters are estimated, and returned.
}
\value{
\command{\link{RFloglikelihood}} returns a list
containing the likelihood, the log likelihood, and
the global variance (if estimated -- see details).
}
\author{Martin Schlather, \email{schlather@math.uni-mannheim.de}
\url{http://ms.math.uni-mannheim.de/de/publications/software}
}
\seealso{
\link{Bayesian},
\command{\link{RMmodel}},
\command{\link{RFfit}},
\command{\link{RFsimulate}},
\command{\link{RFlinearpart}}.
}
\examples{
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
## RFoptions(seed=NA) to make them all random again
require("mvtnorm")
pts <- 5
repet <- 3
model <- RMexp()
x <- runif(n=pts, min=-1, max=1)
y <- runif(n=pts, min=-1, max=1)
data <- as.matrix(RFsimulate(model, x=x, y=y, n=repet, spC = FALSE))
print(cbind(x, y, data))
print(unix.time(likeli <- RFlikelihood(model, x, y, data=data)))
str(likeli, digits=8)
L <- 0
C <- RFcovmatrix(model, x, y)
for (i in 1:ncol(data)) {
print(unix.time(dn <- dmvnorm(data[,i], mean=rep(0, nrow(data)),
sigma=C, log=TRUE)))
L <- L + dn
}
print(L)
stopifnot(all.equal(likeli$log, L))
%--------------------------------------------------------------
pts <- 5
repet <- 1
trend <- 2 * sin(R.p(new="isotropic")) + 3
#trend <- RMtrend(mean=0)
model <- 2 * RMexp() + trend
x <- seq(0, pi, len=10)
data <- as.matrix(RFsimulate(model, x=x, n=repet, spC = FALSE))
print(cbind(x, y, data))
print(unix.time(likeli <- RFlikelihood(model, x, data=data)))
str(likeli, digits=8)
L <- 0
tr <- RFfctn(trend, x=x, spC = FALSE)
C <- RFcovmatrix(model, x)
for (i in 1:ncol(data)) {
print(unix.time(dn <- dmvnorm(data[,i], mean=tr, sigma=C, log=TRUE)))
L <- L + dn
}
print(L)
stopifnot(all.equal(likeli$log, L))
%--------------------------------------------------------------
pts <- c(4, 5)
repet <- c(2, 3)
trend <- 2 * sin(R.p(new="isotropic")) + 3
model <- 2 * RMexp() + trend
x <- y <- data <- list()
for (i in 1:length(pts)) {
x[[i]] <- list(x = runif(n=pts[i], min=-1, max=1),
y = runif(n=pts[i], min=-1, max=1))
data[[i]] <- as.matrix(RFsimulate(model, x=x[[i]]$x, y=x[[i]]$y,
n=repet[i], spC = FALSE))
}
print(unix.time(likeli <- RFlikelihood(model, x, data=data)))
str(likeli, digits=8)
L <- 0
for (p in 1:length(pts)) {
tr <- RFfctn(trend, x=x[[p]]$x, y=x[[p]]$y,spC = FALSE)
C <- RFcovmatrix(model, x=x[[p]]$x, y=x[[p]]$y)
for (i in 1:ncol(data[[p]])) {
print(unix.time(dn <- dmvnorm(data[[p]][,i], mean=tr, sigma=C,
log=TRUE)))
L <- L + dn
}
}
print(L)
stopifnot(all.equal(likeli$log, L))
\dontshow{FinalizeExample()}
}
\keyword{spatial}