prior: Creates prior distribution definitions

Description

The function prior creates a valid prior definition for use in spGGT.

Usage

prior(dist, ...)

Arguments

dist

a quoted key word that identifies the prior distribution. The choices are inverse-gamma "IG", uniform "UNIF", half-Cauchy "HC", normal "NORMAL", flat "FLAT", inverse-Wishart "

...

the hyperparameters of the chosen prior distribution, passed as quoted key words with associated values. See details below.

Value

priora list object of class ggt.prior which is used for the value portion of the prior tag in the spGGT function.

code

spGGT

Details

Up to a proportionality constant the possible priors are:

Uniform:

{$1/(b-a), b > a$, where $b > a$. Use key words "a", and "b". } Inverse-gamma:{$x^{-(a+1)} exp(-b/x)$, where $a$ is shape $> 0$ and $b$ is scale $> 0$. Use key words "shape", and "scale". } Half-Cauchy:{$(x + a^2)^{-1}$. Use key word "a". } Normal:{$exp(-1/2 (\beta - mu)^t V^{-1} (\beta - mu))$, where $mu$ is the mean vector of length $p$ and $V^{-1}$ is the $p \times p$ precision matrix. Use key words "mu" and "precision". }

Inverse-Wishart:{$det(S)^{df/2}det(W)^{-(df+m+1)/2}exp(-1/2 tr(SW^{-1}))$, where $W$ is the $m \times m$ covariance matrix, $df$ is the degrees of freedom, and $S$ is the positive definite $m \times m$ scale matrix. Use key words "df" and "S". }

References

Banerjee, S., Carlin, B.P., and Gelfand, A.E. (2004). Hierarchical modeling and analysis for spatial data. Chapman and Hall/CRC Press, Boca Raton, Fla.

Gelman, A. (2006). Prior distributions for variance parameters in hierarchical models 1(3):515-533, Bayesian Analysis.