hyperparlin: Find Scale Parameter for Inverse Gamma Hyperprior of Linear...

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

Description

This function implements a optimisation routine that computes the scale parameter b and selection parameter r. Here, we assume an inverse gamma prior IG(a,b) for τ^2 and β|δ,τ^2\sim N(0,r(δ)τ^2). For given shape paramter a the user gets b, r such that approximately P(β≤ c2|spike)≥ 1-α2 and P(β≥ c1|slab)≥ 1-α1 hold.
Note that if you observe numerical instabilities try not to specify α1 and α2 smaller than 0.1.

Usage

hyperparlin(alpha1 = 0.1, alpha2 = 0.1, c1 = 0.1, c2 = 0.1,
  eps = .Machine$double.eps, a = 5)

Arguments

alpha1	denotes the 1-α1 level for b.
alpha2	denotes the 1-α2 level for r.
c1	denotes the expected range of the linear effect in the slab part.
c2	denotes the expected range of the linear effect in the spike part.
eps	denotes the error tolerance of the result, default is .Machine$double.eps.
a	is the shape parameter of the inverse gamma distribution, default is 5.

Value

an object of class list with root values r, b from uniroot.

Warning

α1 and α2 should not be smaller than 0.1 due to numerical sensitivity and possible instability. Better change c1, c2.

Author(s)

Nadja Klein

References

Nadja Klein, Thomas Kneib, Stefan Lang and Helga Wagner (2016). Automatic Effect Selection in Distributional Regression via Spike and Slab Priors. Working Paper.

Examples

set.seed(123)
result <- hyperparlin()
r <- result$r
b <- result$b

hyperparlin(alpha1=0.1,alpha2=0.1,c1=0.5,c2=0.1,a=5) 

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