solve_for_hiershrink_scale: Numerical-based solution to the scale parameter c

Description Usage Arguments Value

View source: R/solve_for_hiershrink_scale.R

Description

This function calculates a numerical-based solution to the scale parameter c in the the equation three lines from the top of page 7 in Section 2 of Boonstra and Barbaro. If desired, the user may request regional scale values for a partition of the covariates into two regions, defined by the first npar1 covariates and the second npar2 covariates, but this functionality was not used in Boonstra and Barbaro.

Usage

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
solve_for_hiershrink_scale(
  target_mean1,
  target_mean2 = NA,
  npar1,
  npar2 = 0,
  local_dof = 1,
  regional_dof = -Inf,
  global_dof = 1,
  slab_precision = (1/15)^2,
  n,
  sigma = 2,
  tol = .Machine$double.eps^0.5,
  max_iter = 100,
  n_sim = 2e+05
)

Arguments

target_mean1

(pos. reals): the desired prior number of effective parameters (tilde xi_eff in Boonstra and Barbaro). If one scale parameter is desired, leave target_mean2 = NA. An error will be thrown if target_mean1 > npar1 or if target_mean2 > npar2.

target_mean2

(pos. reals): the desired prior number of effective parameters (tilde xi_eff in Boonstra and Barbaro). If one scale parameter is desired, leave target_mean2 = NA. An error will be thrown if target_mean1 > npar1 or if target_mean2 > npar2.

npar1

(pos. integers): the number of covariates. If one scale parameter is required, then leave npar2 = 0.

npar2

(pos. integers): the number of covariates. If one scale parameter is required, then leave npar2 = 0.

local_dof

(pos. integer) numbers indicating the degrees of freedom for lambda_j and tau, respectively. Boonstra and Barbaro never considered local_dof != 1 or global_dof != 1.

regional_dof

(pos. integer) Not used in Boonstra and Barbaro.

global_dof

(pos. integer) numbers indicating the degrees of freedom for lambda_j and tau, respectively. Boonstra and Barbaro never considered local_dof != 1 or global_dof != 1.

slab_precision

(pos. real) the slab-part of the regularized horseshoe, this is equivalent to (1/d)^2 in the notation of Boonstra and Barbaro

n

(pos. integer) sample size

sigma

(pos. real) square root of the assumed dispersion. In Boonstra and Barbaro, this was always 2, corresponding to the maximum possible value: sqrt(1/[0.5 * (1 - 0.5)]).

tol

(pos. real) numerical tolerance for convergence of solution

max_iter

(pos. integer) maximum number of iterations to run without convergence before giving up

n_sim

(pos. integer) number of simulated draws from the underlying student-t hyperpriors to calculate the Monte Carlo-based approximation of the expectation.

Value

A list containing the following named elements:


umich-biostatistics/AdaptiveBayesianUpdates documentation built on July 29, 2021, 3:06 a.m.