OBASpatial (version 1.9)

nsroba: Bayesian estimation for the NSR model.

Description

This function performs Bayesian estimation of \(\theta=(\bold{\beta},\sigma^2,\phi)\) for the NSR model using the based reference, Jeffreys' rule ,Jeffreys' independent and vague priors.

Usage

nsroba(formula, method="median",
prior = "reference",coords.col = 1:2,kappa = 0.5,
cov.model = "matern", data,asigma=2.1, intphi = "default",
ini.pars, burn=500, iter=5000, thin=10,
cprop = NULL)

Value

$dist

Joint sample (matrix object) obtaining for (\(\bold{beta},\sigma^2,\phi\)).

$betaF

Sample obtained for \(\bold{beta}\).

$sigmaF

Sample obtained for \(\sigma^2\).

$phiF

Sample obtained for \(\phi\).

$coords

Spatial data coordinates.

$kappa

Shape parameter of the covariance function.

$X

Design matrix of the model.

$type

Covariance function of the model.

$theta

Bayesian estimator of (\(\bold{beta},\sigma,\phi\)).

$y

Response variable.

$prior

Prior density considered.

Arguments

formula

A valid formula for a linear regression model.

method

Method to estimate (\(\bold{beta},\sigma,\phi\)). The methods availables are "mean","median" and "mode".

prior

Objective prior densities avaiable for the TSR model: ( reference: Reference based, jef.rul: Jeffreys' rule, jef.ind: Jeffreys' independent, vague, Vague).

coords.col

A vector with the column numbers corresponding to the spatial coordinates.

kappa

Shape parameter of the covariance function (fixed).

cov.model

Covariance functions available for the TSR model. matern: Matern, pow.exp: power exponential, exponential:exponential, cauchy: Cauchy, spherical: Spherical.

data

Data set with 2D spatial coordinates, the response and optional covariates.

asigma

Value of \(a\) for the vague prior.

intphi

An interval for \(\phi\) used for the uniform proposal. See DETAILS below.

ini.pars

Initial values for \((\sigma^2,\phi)\) in that order.

burn

Number of observations considered in the burning process.

iter

Number of iterations for the sampling procedure.

thin

Number of observations considered in the thin process.

cprop

A constant related to the acceptance probability (Default = NULL indicates that cprop is computed as the interval length of intphi). See DETAILS below.

Author

Jose A. Ordonez, Marcos O. Prates, Larissa A. Matos, Victor H. Lachos.

Details

For the "unif" proposal, it was considered the structure where a priori, \(\phi\) follows an uniform distribution on the interval intphi. By default, this interval is computed using the empirical range of data as well as the constant cprop.

For the Jeffreys independent prior, the sampling procedure generates improper posterior distribution when intercept is considered for the mean function.

References

Berger, J.O, De Oliveira, V. and Sanso, B. (2001). Objective Bayesian Analysis of Spatially Correlated Data. Journal of the American Statistical Association., 96, 1361 -- 1374.

See Also

dnsrposoba,dtsrprioroba,dnsrprioroba,tsroba

Examples

# \dontshow{
set.seed(25)
data(dataelev)


######covariance matern: kappa=0.5
res=nsroba(elevation~1, kappa = 0.5, cov.model = "matern", data=dataelev,
ini.pars=c(10,390),iter=2,burn=0,thin=1)

summary(res)

# }


# \donttest{

set.seed(25)
data(dataelev)


######covariance matern: kappa=0.5
res=nsroba(elevation~1, kappa = 0.5, cov.model = "matern", data=dataelev,
ini.pars=c(10,390))

summary(res)

######covariance matern: kappa=1
res1=nsroba(elevation~1, kappa = 1, cov.model = "matern", data=dataelev,
ini.pars=c(10,390))

summary(res1)

######covariance matern: kappa=1.5
res2=nsroba(elevation~1, kappa = 1.5, cov.model = "matern", data=dataelev,
ini.pars=c(10,390))

summary(res2)



# }