sample.nu {DSSP}

Function to sample from the posterior of the spatial effects

Description

This function samples from the posterior density of the spatial effects from the direct sampling spatial prior (DSSP) model.

Usage

sample.nu(Y, eta, delta, EV, V)

Arguments

Y

vector of observed data.

eta

samples of the smoothing parameter from the sample.eta function.

delta

samples of the variance parameter from the sample.delta function.

EV

eigenvalues of the precision matrix spatial prior from the function make.M().

V

eigenvectors of the precision matrix spatial prior from the function make.M().

Value

A matrix of samples with each column a random draw from the posterior of the spatial effects from the DSSP model \pi(nu | eta, delta, y).

Examples

## Use the Meuse River dataset from the package 'gstat'

library(sp)
library(gstat)
data(meuse.all)
coordinates(meuse.all) <- ~ x + y
X <- scale(coordinates(meuse.all))
tmp <- make.M(X)

EV <- tmp$M.eigen$values
V <- tmp$M.eigen$vectors

Y <- scale(log(meuse.all$zinc))
Q <- crossprod(Y, V)

ND <- nrow(X) - 3
f <- function(x) -x ## log-prior for exponential distribution for the smoothing parameter
## Draw 100 samples from the posterior of eta given the data y.

ETA <- sample.eta(100, ND, EV, Q, f, UL = 1000)
DELTA <- sample.delta(ETA, ND, EV, Q, pars = c(0.001, 0.001))
NU <- sample.nu(Y, ETA, DELTA, EV, V)