View source: R/prinfunctions.R
intmnorm | R Documentation |
It calculates the marginal density density for a model M (up to a proportionality constant) for the NSR model using the based reference, Jeffreys' rule, Jeffreys' independent and vague priors. In this context φ corresponds to the range parameter.
intmnorm(formula,prior="reference",coords.col=1:2,kappa=0.5, cov.model="exponential",data,asigma=2.1,intphi,maxEval)
formula |
A valid formula for a linear regression model. |
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. |
asigma |
Value of a for vague prior. |
intphi |
An interval for φ used for vague prior. |
maxEval |
Maximum number of iterations for the integral computation. |
Let m_k a parametric model with parameter vector θ_k. Under the TSR model and the prior density proposal:
\frac{π(φ)}{(σ^2)^a}
we have that the marginal density is given by:
\int L(θ_{m_k})π(m_k)dm_k
This quantity can be useful as a criteria for model selection. The computation of m_k could be compute demanding depending on the number of iterations in maxEval
.
Marginal density of the model m_k for the reference based, Jeffreys' rule, Jeffreys' independent and vague priors.
Jose A. Ordonez, Marcos O. Prates, Larissa A. Matos, Victor H. Lachos.
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.
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data(dataca20) set.seed(25) data(dataelev)## data using by Berger et. al (2001) ######### Using reference prior ########### m1=intmnorm(prior="reference",formula=elevation~1, kappa=0.5,cov.model="matern",data=dataelev,maxEval=1000) log(m1) ######### Using reference prior kappa=1 ########### m2=intmnorm(prior="reference",formula=elevation~1, kappa=1,cov.model="matern",data=dataelev,maxEval=1000) log(m2) ######### Using reference prior kappa=1.5 ########### m3=intmnorm(prior="reference",formula=elevation~1 ,kappa=1.5,cov.model="matern",data=dataelev,maxEval=1000) log(m3) tot=m1+m2+m3 ########posterior probabilities: higher probability: #########prior="reference", kappa=1 p1=m1/tot p2=m2/tot p3=m3/tot
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