This function performs conditional simulation (by MCMC) in a generalised linear spatial model for fixed parameters.
glsm.mcmc(geodata, coords = geodata$coords, data = geodata$data,
units.m = "default", model, mcmc.input, messages)a list containing elements coords and
data as described next.
Typically an object of the class "geodata" - a geoR data set.
If not provided the arguments coords and data must be provided instead.
The list may also contain an argument units.m as described
below.
an \(n \times 2\) matrix, each row containing Euclidean
coordinates of the n data locations. By default it takes the
element coords of the argument geodata.
a vector with data values. By default it takes the
element data of the argument geodata.
\(n\)-dimensional vector of observation times for the data. By default (units.m = "default"),
it takes geodata$units.m in case this exist and else a vector of 1's.
defines the model components. Either an object of
class likGLSM; typically output from
likfit.glsm, or a list containing
the arguments :
trendspecifies the trend (covariate) values at the data
locations. See documentation of trend.spatial
for further details.
Default is trend = "cte".
betanumerical value of the mean (vector) parameter.
cov.modelstring indicating the name of the model for the
correlation function. Further details in the
documentation for cov.spatial.
cov.parsa vector with the 2 covariance parameters \(\sigma^2\), and \(\phi\) for the underlying Gaussian field.
kappaadditional smoothness parameter required by the following correlation
functions: "matern", "powered.exponential", "cauchy" and
"gneiting.matern".
nuggetthe value of the nugget parameter
\(\tau^2\) for the underlying Gaussian field. Default is
nugget = 0.
aniso.parsparameters for geometric anisotropy
correction. If aniso.pars = FALSE no correction is made, otherwise
a two elements vector with values for the anisotropy parameters
must be provided. Anisotropy correction consists of a
transformation of the data and prediction coordinates performed
by the function coords.aniso.
familyequal to either "poisson" or
"binomial"
linkequal to either "canonical" (default), "log",
"boxcox" or "logit". For "canonical" then
in general
the canonical link function is used ("log" for the
Poisson distribution and "logit" for the binomial distribution), but when
lambda is also specified then the Box-Cox class is used
(a mis-use of the terminology "canonical", really).
lambdanumeric value of the Box-Cox transformation parameter.
The value \(\lambda = 1\) corresponds to
no transformation and the default value \(\lambda = 0\) corresponds to
the log-transformation. Only used when family = "poisson"
input parameter for the MCMC algorithm. It can take an output from mcmc.control or
a list with elements as for the arguments in
mcmc.control. See documentation for
mcmc.control. ATTENTION: the argument S.scale is necessary while
all the others have default values.
logical. Indicates whether or not status messages are printed on the screen (or other output device) while the function is running.
A list with the following components:
an \(n \times n.sim\) matrix with \(n.sim\) being the number of MCMC simulations. containing \(S_i\). Each column corresponds to a conditional simulation of the conditional distribution of \(S_i\) at the data locations.
matrix with acceptance rates from MCMC. Only returned when no prediction locations are given.
Information about the model parameters, link function and error distribution family used.
Information about the data.
the function call.
For simulating the conditional distribution of \(S\) given \(y\), the Langevin-Hastings algorithm with the parametrisation in Papaspilliopoulus, Roberts and Skold (2003) is used. This algorithm is a Metropolis-Hastings algorithm, where the proposal distribution uses gradient information from the log-posterior distribution.
The proposal variance (called S.scale; see mcmc.control)
for the algorithm needs to be scaled
such that approximately 60 percent of the proposals are accepted. We
also recommend that the user to studies plots of the autocorrelations.
O. Papaspiliopoulus and G. O. Roberts and M. Skold (2003). Non-centered parameterizations for hierarchical models and data augmentation. Bayesian statistics 7 (eds. J. M. Bernardo, S. Bayarri, J. O. Berger, A. P. Dawid, D. Heckerman, A. F. M. Smith and M. West), Oxford University Press, 307-326.
binom.krige for prediction with fixed parameters in the
Binomial-normal model, pois.krige for prediction with fixed parameters in the
Poisson normal model.
# NOT RUN {
if(!exists(".Random.seed", envir=.GlobalEnv, inherits = FALSE)) set.seed(1234)
data(b50)
test <- glsm.mcmc(b50, model = list(family="binomial",
cov.pars = c(1,1), beta = c(1,0), trend =~ rnorm(50),
cov.model="spherical", nugget=0.3),
mcmc.input = mcmc.control(S.scale = 0.2, thin = 1))
## visulalising the MCMC output using the coda package
test.coda <- create.mcmc.coda(test, mcmc.input = list(thin = 1))
library(coda)
# }
# NOT RUN {
plot(test.coda)
autocorr.plot(test.coda)
# }
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