get_theta_aunif: Find Scale Parameter for Hyperprior for Variances Where the...

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

Description

This function implements a optimisation routine that computes the scale parameter θ of the prior τ^2 (corresponding to a differentiably approximated version of the uniform prior for τ) for a given design matrix and prior precision matrix such that approximately P(|f(x_{k}|≤ c,k=1,…,p)≥ 1-α

Usage

get_theta_aunif(alpha = 0.01, method = "integrate", Z, c = 3,
  eps = .Machine$double.eps, Kinv)

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.

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.

Andrew Gelman (2006). Prior Distributions for Variance Parameters in Hierarchical Models. Bayesian Analysis, 1(3), 515–533.

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)$Z_B,nrow=1)
theta <- get_theta_aunif(alpha = 0.01, method = "integrate", Z = Z, 
                            c = 3, eps = .Machine$double.eps, Kinv = Kinv)$root

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