sdPrior (version 1.0-0)

mdf_ga: Marginal Density for Given Scale Parameter and Half-Normal Prior for \(\tau\)

Description

This function computes the marginal density of \(z_p'\beta\) for gamma priors for \(\tau^2\) (referring to a half-normal prior for \(\tau\)).

Usage

mdf_ga(f, theta, Z, Kinv)

Arguments

f

point the marginal density to be evaluated at.

theta

denotes the scale parameter of the gamma hyperprior for \(\tau^2\) (half-normal for \(\tau\)).

Z

the row of the design matrix evaluated.

Kinv

the generalised inverse of K.

Value

the marginal density evaluated at point x.

References

Nadja Klein and Thomas Kneib (2015). Scale-Dependent Priors for Variance Parameters in Structured Additive Distributional Regression. Working Paper.

Examples

# NOT RUN {
set.seed(123)
library(MASS)
# prior precision matrix (second order differences) 
# of a spline of degree l=3 and with m=20 inner knots
# yielding dim(K)=m+l-1=22
K <- t(diff(diag(22), differences=2))%*%diff(diag(22), differences=2)
# generalised inverse of K
Kinv <- ginv(K)
# covariate x
x <- runif(1)
Z <- matrix(DesignM(x)$Z_B,nrow=1)
fgrid <- seq(-3,3,length=1000)
mdf <- mdf_ga(fgrid,theta=0.0028,Z=Z,Kinv=Kinv)

# }