DSSP {DSSP}

DSSP

Description

This function samples from the log-posterior of all parameters in the model and returns a list object containing the samples. It performs a few compatibility checks on the inputs, then calls the sample.eta(), sample.delta(), and sample.nu().

Usage

DSSP(formula, data, N, pars, log_prior = function(x) -x, coords = NULL)

Arguments

formula

a two sided linear formula with the response on left and the covariates on the right.

data

a data.frame or sp::SpatialPointsDataFrame containing the response variable, covariates and coordinates.

N

is the number of random samples to be drawn from the joint posterior for eta, delta, and nu.

pars

a vector of the prior shape and rate parameters for the inverse-gamma prior distribution of delta, the variance parameter for the Gaussian likelihood.

log_prior

a function evaluating the log of the prior density of eta. Default to be function(x) -x.

coords

spatial coordinates passed as the value argument to sp::coordinates().

Details

The direct sampling spatial prior model assumes that the spatial model can be written as the likelihood parameterised with mean vector nu and variance delta

(y | nu, delta) ~ N(nu, delta * I)

where I is the identity matrix. The prior for the vector of spatial effects nu is improper but is proportional to

\pi(nu | eta) propto (det(M)/2\pi)^{1/2} * exp(-eta nu' M nu/2),

the prior for delta is assumed to be a inverse-gamma distribution

(delta) ~ IG(a,b)

and the prior for eta can be specified for the user as any valid density function for eta > 0.

Value

A list containing N samples of nu, eta, delta, and the original data X and Y.

Examples

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

library(sp)
library(gstat)
data(meuse.all)
coordinates(meuse.all) <- ~ x + y

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.
OUTPUT <- DSSP(
  formula = log(zinc) ~ 1, data = meuse.all, N = 100,
  pars = c(0.001, 0.001), log_prior = f
)