dtsrprioroba: Objective prior density for the TSR model

In OBASpatial: Objective Bayesian Analysis for Spatial Regression Models

Objective prior 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 and Jeffreys' independent priors. In this context φ corresponds to the range parameter and ν to the degrees of freedom.

Usage

dtsrprioroba(x,trend="cte",prior="reference",coords.col=1:2,
kappa=0.5,cov.model="exponential",data)

Arguments

x	A vector with the quanties (φ,ν)
trend	Builds the trend matrix in accordance to a specification of the mean provided by the user. See DETAILS below.
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

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 μ(\bold{c})=μ is constant over the region.

• "1st", the design matrix is such that mean function becames a first order polynomial on the coordinates:

  μ(\bold(c))=β_0+ β_1c_1+β_2c_2

• "2nd", the design matrix is such that mean function μ(\bold{c})=μ becames a second order polynomial on the coordinates:

  μ(\bold(c))=β_0+ β_1c_1+β_2c_2 + β_3c_{1}^2+ β_4c_{2}^2+ β_5c_1c_2

• ~model a model specification to include covariates (external trend) in the model.

Value

Density of x=(φ,ν)

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

dtsrposoba,dnsrprioroba,dnsrposoba

Examples

data(dataca20)

######### Using reference prior and a constant trend###########
dtsrprioroba(x=c(6,100),kappa=0.3,cov.model="matern",data=dataca20)


######### Using jef.rule prior and 1st trend###########
dtsrprioroba(x=c(6,100),prior="jef.rul",trend=~altitude+area,
kappa=0.3,cov.model="matern",data=dataca20)

######### Using  jef.ind prior ###########
dtsrprioroba(x=c(6,100),prior="jef.ind",trend=0,
kappa=0.3,cov.model="matern",data=dataca20)

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