dnsrprioroba {OBASpatial} | R Documentation |
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)
Arguments
x |
The |
trend |
Builds the trend matrix in accordance to a specification of the mean provided by the user. See |
prior |
Objective prior densities avaiable for the TSR model: ( |
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. |
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\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.
Value
Prior density of x=\phi
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)