View source: R/prinfunctions.R
dtsrposoba | R Documentation |
It calculates the density function π(φ,ν) (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.
dtsrposoba(x,formula,prior="reference",coords.col=1:2, kappa=0.5,cov.model="exponential",data,asigma=2.1,intphi,intnu)
x |
A vector with the quanties (φ,ν). For the vague prior x must be a three dimension vector (φ,ν,λ) with λ a number in the interval (0.02,0.5). See |
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. |
The posterior distribution is computed for this priors under the improper family \frac{π(φ,ν)}{(σ^2)^a}. For the vague prior, it was considered the structure π(φ,ν,λ)=φ(φ)π(ν|λ)π(λ) where a priori, φ follows an uniform distribution on the interval intphi
, ν|λ~ Texp(λ,A) with A the interval given by the argument intnu
and λ~unif(0.02,0.5).
For the Jeffreys independent prior, this family of priors generates improper posterior distribution when intercept is considered for the mean function.
Posterior density of x=(φ,ν) for the reference based, Jeffreys' rule and Jeffreys' independent priors. For the vague the result is the posterior density of x=(φ,ν,λ)
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).
dnsrposoba
,dtsrprioroba
,dnsrprioroba
data(dataca20) ######### Using reference prior ########### dtsrposoba(x=c(5,11),prior="reference",formula=calcont~altitude+area, kappa=0.3,cov.model="matern",data=dataca20) ######### Using Jeffreys' rule prior ########### dtsrposoba(x=c(5,11),prior="jef.rul",formula=calcont~altitude+area, kappa=0.3,cov.model="matern",data=dataca20) ######### Using Jeffreys' independent prior ########### dtsrposoba(x=c(5,11),prior="jef.ind",formula=calcont~altitude+area ,kappa=0.3,cov.model="matern",data=dataca20) ######### Using vague independent prior ########### dtsrposoba(x=c(5,11,.3),prior="vague",formula=calcont~altitude+area, kappa=0.3,cov.model="matern",data=dataca20,intphi=c(0.1,10), intnu=c(4.1,30))
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