DSSP (version 0.1.1)

sample.eta: Function to sample from the posterior of the smoothing parameter eta conditioned on the data y.

Description

This function samples from the log-posterior density of the smoothing parameter from the thin-plate splines based spatial prior using a ratio-of-uniform sampler.

Usage

sample.eta(N, ND, EV, Q, UL = 1000, log_prior)

Value

N samples drawn from the posterior of eta given the data y \(\pi(eta | y)\).

Arguments

N

the number of samples desired.

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.

UL

the upper limit for the smoothing parameter value; used for the ratio-of-uniform sampler, default is 1000.

log_prior

a function of x evaluating the log of the prior density for eta

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

M <- tmp$M

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.
sample.eta(100, ND, EV, Q, UL = 1000, f)