get_theta_ig: Find Scale Parameter for Inverse Gamma Hyperprior

In sdPrior: Scale-Dependent Hyperpriors in Structured Additive Distributional Regression

Description

This function implements a optimisation routine that computes the scale parameter b of the inverse gamma prior for τ^2 when a=b=ε with ε small for a given design matrix and prior precision matrix such that approximately P(|f(x_{k}|≤ c,k=1,…,p)≥ 1-α When a unequal to a the shape parameter a has to be specified.

Usage

get_theta_ig(alpha = 0.01, method = "integrate", Z, c = 3,
  eps = .Machine$double.eps, Kinv, equals = FALSE, a = 1,
  type = "marginalt")

Arguments

alpha	denotes the 1-α level.
method	with integrate as default. Currently no further method implemented.
Z	the design matrix.
c	denotes the expected range of the function.
eps	denotes the error tolerance of the result, default is .Machine$double.eps.
Kinv	the generalised inverse of K.
equals	saying whether a=b. The default is FALSE due to the fact that a is a shape parameter.
a	is the shape parameter of the inverse gamma distribution, default is 1.
type	is either numerical integration (integrate) of to obtain the marginal distribution of z_p'β or the theoretical marginal t-distribution (marginalt). marginalt is the default value.

Details

Currently, the implementation only works properly for the cases a unequal b.

Value

an object of class list with values from uniroot.

Author(s)

Nadja Klein

References

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

Stefan Lang and Andreas Brezger (2004). Bayesian P-Splines. Journal of Computational and Graphical Statistics, 13, 183-212.

Examples

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)$Z_B,nrow=1)
theta <- get_theta_ig(alpha = 0.01, method = "integrate", Z = Z, 
                      c = 3, eps = .Machine$double.eps, Kinv = Kinv, 
					 equals = FALSE, a = 1, type="marginalt")$root

sdPrior documentation built on May 2, 2019, 8:57 a.m.