View source: R/prinfunctions.R
intmT | R Documentation |
It calculates the marginal density density for a model M (up to a proportionality constant) for the TSR model using the based reference, Jeffreys' rule, Jeffreys' independent and vague priors. In this context φ corresponds to the range parameter and ν to the degrees of freedom.
intmT(formula,prior="reference",coords.col=1:2,kappa=0.5, cov.model="exponential",data,asigma,intphi="default",intnu=c(4.1,Inf),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. |
intnu |
An interval for ν 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,ν)}{(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.
Ordonez, J.A, M.O. Prattes, L.A. Matos, and V.H. Lachos (2020+). Objective Bayesian analysis for spatial Student-t regression models (Submitted).
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set.seed(25) data(dataca20) ######### Using reference prior ########### m1=intmT(prior="reference",formula=calcont~altitude+area, kappa=0.3,cov.model="matern",data=dataca20,maxEval=1000) ######### Using Jeffreys' rule prior ########### m1j=intmT(prior="jef.rul",formula=calcont~altitude+area, kappa=0.3,cov.model="matern",data=dataca20,maxEval=1000) ######### Using Jeffreys' independent prior ########### m1ji=intmT(prior="jef.ind",formula=calcont~altitude+area ,kappa=0.3,cov.model="matern",data=dataca20,maxEval=1000) m1v=intmT(prior="vague",formula=calcont~altitude+area ,kappa=0.3,cov.model="matern",data=dataca20,maxEval=1000,intphi="default") tot=m1+m1j+m1ji+m1v ########posterior probabilities: higher probability: #########prior="reference", kappa=0.3 p1=m1/tot pj=m1j/tot pji=m1ji/tot pv=m1v/tot
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