dtsrposoba: Objective posterior density for the TSR model

In OBASpatial: Objective Bayesian Analysis for Spatial Regression Models

Objective posterior density for the TSR model

Description

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.

Usage

dtsrposoba(x,formula,prior="reference",coords.col=1:2,
kappa=0.5,cov.model="exponential",data,asigma=2.1,intphi,intnu)

Arguments

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 DETAILS below.
formula	A valid formula for a linear regression model.
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.
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.

Details

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.

Value

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)

Author(s)

Jose A. Ordonez, Marcos O. Prates, Larissa A. Matos, Victor H. Lachos.

References

Ordonez, J.A, M.O. Prattes, L.A. Matos, and V.H. Lachos (2020+). Objective Bayesian analysis for spatial Student-t regression models (Submitted).

See Also

dnsrposoba,dtsrprioroba,dnsrprioroba

Examples

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))

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