OBASpatial (version 1.9)

dnsrprioroba: Objective prior density for the NSR model

Description

It calculates the density function \(\pi(\phi)\) (up to a proportionality constant) for the NSR model using the based reference, Jeffreys' rule and Jeffreys' independent priors. In this context \(\phi\) corresponds to the range parameter.

Usage

dnsrprioroba(x,trend="cte",prior="reference",coords.col=1:2,
kappa=0.5,cov.model="exponential",data)

Value

Prior density of x=\(\phi\)

Arguments

x

The \(\phi\) quantil value.

trend

Builds the trend matrix in accordance to a specification of the mean provided by the user. See DETAILS below.

prior

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

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.

Author

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

Details

Denote as \(\bold{c}=(c_{1},c_{2})\) the coordinates of a spatial location. trend defines the design matrix as:

• 0 (zero,without design matrix) Only valid for the Independent Jeffreys' prior

• "cte", the design matrix is such that mean function \(\mu(\bold{c})=\mu\) is constant over the region.

• "1st", the design matrix is such that mean function becames a first order polynomial on the coordinates: $$\mu(\bold(c))=\beta_0+ \beta_1c_1+\beta_2c_2$$

• "2nd", the design matrix is such that mean function \(\mu(\bold{c})=\mu\) becames a second order polynomial on the coordinates: $$\mu(\bold(c))=\beta_0+ \beta_1c_1+\beta_2c_2 + \beta_3c_{1}^2+ \beta_4c_{2}^2+ \beta_5c_1c_2$$

• ~model a model specification to include covariates (external trend) in the model.

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

dtsrposoba,dtsrprioroba,dnsrposoba

Examples

data(dataelev)## data using by Berger et. al (2001)

######### Using reference prior ###########
dnsrprioroba(x=20,kappa=0.3,cov.model="matern",data=dataelev)


######### Using jef.rule prior###########
dnsrprioroba(x=20,prior="jef.rul",kappa=0.3,cov.model="matern",
data=dataelev)

######### Using  jef.ind prior ###########
dnsrprioroba(x=20,prior="jef.ind",trend=0,
kappa=0.3,cov.model="matern",data=dataelev)