nsroba: Bayesian estimation for the NSR model.

In OBASpatial: Objective Bayesian Analysis for Spatial Regression Models

Bayesian estimation for the NSR model.

Description

This function performs Bayesian estimation of θ=(\bold{β},σ^2,φ) 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)

Arguments

formula	A valid formula for a linear regression model.
method	Method to estimate (\bold{beta},σ,φ). 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 φ used for the uniform proposal. See DETAILS below.
ini.pars	Initial values for (σ^2,φ) 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.

Details

For the "unif" proposal, it was considered the structure where a priori, φ 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.

Value

$dist	Joint sample (matrix object) obtaining for (\bold{beta},σ^2,φ).
$betaF	Sample obtained for \bold{beta}.
$sigmaF	Sample obtained for σ^2.
$phiF	Sample obtained for φ.
$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},σ,φ).
$y	Response variable.
$prior	Prior density considered.

Author(s)

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

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

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)

OBASpatial documentation built on Sept. 11, 2022, 9:05 a.m.