get_theta_linear {sdPrior}

Find Scale Parameter for Inverse Gamma Hyperprior of Linear Effects with Spike and Slab Prior

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 \tau^2 when \tau^2\sim N(0,r(\delta)\tau^2) and given shape paramter such that approximately P(\beta\le c_2|spike)\ge 1-\alpha_2 and P(\beta\ge c_1|slab)\ge 1-\alpha1.
\alpha_1 and \alpha_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-\alpha_1 level for v_2.

alpha2

denotes the 1-\alpha_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

\alpha_1 and \alpha_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)