dnsrprioroba: Objective prior density for the NSR model

In OBASpatial: Objective Bayesian Analysis for Spatial Regression Models

Objective prior density for the NSR model

Description

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

Usage

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

Arguments

x	The φ 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.

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 μ(\bold{c})=μ is constant over the region.

• "1st", the design matrix is such that mean function becames a first order polynomial on the coordinates:

  μ(\bold(c))=β_0+ β_1c_1+β_2c_2

• "2nd", the design matrix is such that mean function μ(\bold{c})=μ becames a second order polynomial on the coordinates:

  μ(\bold(c))=β_0+ β_1c_1+β_2c_2 + β_3c_{1}^2+ β_4c_{2}^2+ β_5c_1c_2

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

Value

Prior density of x=φ

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

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)

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