HSreg: Regularized Horseshoe

In abnormally-distributed/Bayezilla: Bayesian Models With JAGS and Several Utilities for Data Exploration and Model Evaluation.

Description

This is the horseshoe model described by Piironen & Vehtari (2017). This tends to run very quickly even for larger data sets or larger numbers of predictors and in my experience is faster and more stable (at least on the tested data sets!) than the same model implemetned in Stan. If the horseshoe+ is analagous to the adaptive Bayesian LASSO, then this could be compared to the Bayesian Elastic Net in that it imposes a combination of different shrinkage penalties (the elastic net being a combination of L1 and L2, and the regularized horseshoe being a combination of sub-L1 and student-t penalties).

Model Specification:

Plugin Pseudo-Variances:

Usage

HSreg(formula, data, family = "gaussian", phi = 0.5, slab_scale = 2,
  slab_df = 3, log_lik = FALSE, iter = 10000, warmup = 4000,
  adapt = 5000, chains = 4, thin = 1, method = "parallel",
  cl = makeCluster(2), ...)

Arguments

formula	the model formula
data	a data frame.
family	one of "gaussian", "binomial", or "poisson".
phi	your prior guess on the inclusion probability. Defaults to .50. Best way to come up with a figure is a prior guess on how many coefficients are non-zero out of the total number of predictors.
slab_scale	the standard deviation of the "slab". Defaults to 2.
slab_df	the degrees of freedom fo the slab. Higher degrees of freedom give increased L2-like regularization. Defaults to 3.
log_lik	Should the log likelihood be monitored? The default is FALSE.
iter	How many post-warmup samples? Defaults to 10000.
warmup	How many warmup samples? Defaults to 1000.
adapt	How many adaptation steps? Defaults to 2000.
chains	How many chains? Defaults to 4.
thin	Thinning interval. Defaults to 1.
method	Defaults to "rjparallel". For an alternative parallel option, choose "parallel" or. Otherwise, "rjags" (single core run).
cl	Use parallel::makeCluster(# clusters) to specify clusters for the parallel methods. Defaults to two cores.
...	Other arguments to run.jags.

Value

an rjags object

References

Piironen, Juho; Vehtari, Aki. Sparsity information and regularization in the horseshoe and other shrinkage priors. Electron. J. Statist. 11 (2017), no. 2, 5018–5051. doi:10.1214/17-EJS1337SI. https://projecteuclid.org/euclid.ejs/1513306866

Carvalho, C. M., Polson, N. G., and Scott, J. G. (2010). The horseshoe estimator for sparse signals. Biometrika, 97(2):465–480.

Examples

HSreg()

abnormally-distributed/Bayezilla documentation built on Oct. 31, 2019, 1:57 a.m.