bayesGeostatExact: Simple Bayesian spatial linear model with fixed semivariogram...

In spBayes: Univariate and Multivariate Spatial-Temporal Modeling

Simple Bayesian spatial linear model with fixed semivariogram parameters

Description

Given a observation coordinates and fixed semivariogram parameters the bayesGeostatExact function fits a simple Bayesian spatial linear model.

Usage

  bayesGeostatExact(formula, data = parent.frame(), n.samples,
                     beta.prior.mean, beta.prior.precision,
                     coords, cov.model="exponential", phi, nu, alpha,
                     sigma.sq.prior.shape, sigma.sq.prior.rate,
                     sp.effects=TRUE, verbose=TRUE, ...)

Arguments

formula	for a univariate model, this is a symbolic description of the regression model to be fit. See example below.
data	an optional data frame containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which spLM is called.
n.samples	the number of posterior samples to collect.
beta.prior.mean	beta multivariate normal mean vector hyperprior.
beta.prior.precision	beta multivariate normal precision matrix hyperprior.
coords	an n x 2 matrix of the observation coordinates in R^2 (e.g., easting and northing).
cov.model	a quoted key word that specifies the covariance function used to model the spatial dependence structure among the observations. Supported covariance model key words are: "exponential", "matern", "spherical", and "gaussian". See below for details.
phi	the fixed value of the spatial decay.
nu	if cov.model is "matern" then the fixed value of the spatial process smoothness must be specified.
alpha	the fixed value of the ratio between the nugget tau.sq and partial-sill sigma.sq parameters from the specified cov.model.
sigma.sq.prior.shape	sigma.sq (i.e., partial-sill) inverse-Gamma shape hyperprior.
sigma.sq.prior.rate	sigma.sq (i.e., partial-sill) inverse-Gamma 1/scale hyperprior.
sp.effects	a logical value indicating if spatial random effects should be recovered.
verbose	if TRUE, model specification and progress of the sampler is printed to the screen. Otherwise, nothing is printed to the screen.
...	currently no additional arguments.

Value

An object of class bayesGeostatExact, which is a list with the following tags:

p.samples	a coda object of posterior samples for the defined parameters.
sp.effects	a matrix that holds samples from the posterior distribution of the spatial random effects. The rows of this matrix correspond to the n point observations and the columns are the posterior samples.
args	a list with the initial function arguments.

Author(s)

Sudipto Banerjee [e-mail],
Andrew O. Finley [e-mail]

Examples

## Not run: 

data(FBC07.dat)
Y <- FBC07.dat[1:150,"Y.2"]
coords <- as.matrix(FBC07.dat[1:150,c("coord.X", "coord.Y")])

n.samples <- 500
n = length(Y)
p = 1

phi <- 0.15
nu <- 0.5

beta.prior.mean <- as.matrix(rep(0, times=p))
beta.prior.precision <- matrix(0, nrow=p, ncol=p)

alpha <- 5/5

sigma.sq.prior.shape <- 2.0
sigma.sq.prior.rate <- 5.0

##############################
##Simple linear model with
##the default exponential
##spatial decay function
##############################
set.seed(1)
m.1 <- bayesGeostatExact(Y~1, n.samples=n.samples,
                          beta.prior.mean=beta.prior.mean,
                          beta.prior.precision=beta.prior.precision,
                          coords=coords, phi=phi, alpha=alpha,
                          sigma.sq.prior.shape=sigma.sq.prior.shape,
                          sigma.sq.prior.rate=sigma.sq.prior.rate)



print(summary(m.1$p.samples))

##Requires MBA package to
##make surfaces
library(MBA)
par(mfrow=c(1,2))
obs.surf <-
  mba.surf(cbind(coords, Y), no.X=100, no.Y=100, extend=T)$xyz.est
image(obs.surf, xaxs = "r", yaxs = "r", main="Observed response")
points(coords)
contour(obs.surf, add=T)

w.hat <- rowMeans(m.1$sp.effects)
w.surf <-
  mba.surf(cbind(coords, w.hat), no.X=100, no.Y=100, extend=T)$xyz.est
image(w.surf, xaxs = "r", yaxs = "r", main="Estimated random effects")
points(coords)
contour(w.surf, add=T)


##############################
##Simple linear model with
##the matern spatial decay
##function. Note, nu=0.5 so
##should produce the same
##estimates as m.1
##############################
set.seed(1)
m.2 <- bayesGeostatExact(Y~1, n.samples=n.samples,
                          beta.prior.mean=beta.prior.mean,
                          beta.prior.precision=beta.prior.precision,
                          coords=coords, cov.model="matern",
                          phi=phi, nu=nu, alpha=alpha,
                          sigma.sq.prior.shape=sigma.sq.prior.shape,
                          sigma.sq.prior.rate=sigma.sq.prior.rate)

print(summary(m.2$p.samples))

##############################
##This time with the
##spherical just for fun
##############################
m.3 <- bayesGeostatExact(Y~1, n.samples=n.samples,
                          beta.prior.mean=beta.prior.mean,
                          beta.prior.precision=beta.prior.precision,
                          coords=coords, cov.model="spherical",
                          phi=phi, alpha=alpha,
                          sigma.sq.prior.shape=sigma.sq.prior.shape,
                          sigma.sq.prior.rate=sigma.sq.prior.rate)

print(summary(m.3$p.samples))

##############################
##Another example but this
##time with covariates
##############################
data(FORMGMT.dat)

n = nrow(FORMGMT.dat)
p = 5 ##an intercept an four covariates

n.samples <- 50

phi <- 0.0012

coords <- cbind(FORMGMT.dat$Longi, FORMGMT.dat$Lat)
coords <- coords*(pi/180)*6378

beta.prior.mean <- rep(0, times=p)
beta.prior.precision <- matrix(0, nrow=p, ncol=p)

alpha <- 1/1.5

sigma.sq.prior.shape <- 2.0
sigma.sq.prior.rate <- 10.0

m.4 <-
  bayesGeostatExact(Y~X1+X2+X3+X4, data=FORMGMT.dat, n.samples=n.samples,
                     beta.prior.mean=beta.prior.mean,
                     beta.prior.precision=beta.prior.precision,
                     coords=coords, phi=phi, alpha=alpha,
                     sigma.sq.prior.shape=sigma.sq.prior.shape,
                     sigma.sq.prior.rate=sigma.sq.prior.rate)

print(summary(m.4$p.samples))



##Requires MBA package to
##make surfaces
library(MBA)
par(mfrow=c(1,2))
obs.surf <-
  mba.surf(cbind(coords, resid(lm(Y~X1+X2+X3+X4, data=FORMGMT.dat))),
                 no.X=100, no.Y=100, extend=TRUE)$xyz.est
image(obs.surf, xaxs = "r", yaxs = "r", main="Observed response")
points(coords)
contour(obs.surf, add=T)

w.hat <- rowMeans(m.4$sp.effects)
w.surf <-
  mba.surf(cbind(coords, w.hat), no.X=100, no.Y=100, extend=TRUE)$xyz.est
image(w.surf, xaxs = "r", yaxs = "r", main="Estimated random effects")
contour(w.surf, add=T)
points(coords, pch=1, cex=1)



## End(Not run)

spBayes documentation built on May 17, 2022, 5:07 p.m.