sample.delta {DSSP}

Function to sample from the posterior of the variance parameter

Description

This function samples from the log-posterior density of the variance parameter from the likelihood

Usage

sample.delta(eta, ND, EV, Q, pars)

Arguments

eta

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

ND

the rank of the precision matrix, the default value is n-3 for spatial data.

EV

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

Q

the data vector from the cross-product of observed data, Y, and eigenvalues from the M matrix, V.

pars

a vector of the prior shape and rate parameters for the inverse-gamma prior distribution of delta.

Value

N samples drawn from the posterior of \pi(delta | eta, 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)

M <- tmp$M

Y <- scale(log(meuse.all$zinc))

ND <- nrow(X) - 3
M.list <- make.M(X) ##  Only Needs to return the eigenvalues and vectors
M <- M.list$M
EV <- M.list$M.eigen$values
V <- M.list$M.eigen$vectors
Q <- crossprod(Y, V)

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))
##  Old Slow Version of sample.nu()
## sample.delta<-function(eta,nd,ev,Q,pars)
## {
##   N<-length(eta)
##   f.beta<-function(x)
##   {
##     lambda<-1/(1+x*ev)
##     b<-tcrossprod(Q,diag(1-lambda))
##     beta<-0.5*tcrossprod(Q,b)+pars[2]
##     return(beta)
##   }
##   alpha<-pars[1]+nd*0.5
##   beta<-sapply(eta,f.beta)
##   delta<-1/rgamma(N,shape=alpha,rate=beta)
##   return(delta)
## }