get_theta_linear: 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 v_2 and selection parameter r of the inverse gamma prior IG(v_1,v_2) for τ^2 when τ^2\sim N(0,r(δ)τ^2) and given shape paramter such that approximately P(β≤ c_2|spike)≥ 1-α_2 and P(β≥ c_1|slab)≥ 1-α1.
α_1 and α_2 should not be smaller than 0.1 due to numerical sensitivity and possible instability. Better change c_1, c_2.

Usage

get_theta_linear(alpha1 = 0.1, alpha2 = 0.1, c1 = 0.1, c2 = 0.1,
  eps = .Machine$double.eps, v1 = 5)

Arguments

alpha1	denotes the 1-α_1 level for v_2.
alpha2	denotes the 1-α_2 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.
v1	is the shape parameter of the inverse gamma distribution, default is 5.

Value

an object of class list with values from uniroot.

Warning

α_1 and α_2 should not be smaller than 0.1 due to numerical sensitivity and possible instability. Better change c_1, c_2.

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 <- get_theta_linear()
r <- result$r
v2 <- result$v2

get_theta_linear(alpha1=0.1,alpha2=0.1,c1=0.5,c2=0.1,v1=5) 

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