sdPrior (version 1.0-0)

get_theta_linear: 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 \(c_1\), \(c_2\).

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

# NOT RUN {
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) 

# }