horseshoe_mcmc: Horseshoe MCMC Sampler for Multiply-Imputed Regression

In BMIselect: Bayesian MI-LASSO for Variable Selection on Multiply-Imputed Datasets

Horseshoe MCMC Sampler for Multiply-Imputed Regression

Description

Implements Bayesian variable selection using the hierarchical Horseshoe prior across multiply-imputed datasets. This model applies global–local shrinkage to regression coefficients via a global scale (tau2), local scales (lambda2), and auxiliary hyperpriors (kappa, eta).

Usage

horseshoe_mcmc(
  X,
  Y,
  intercept = TRUE,
  nburn = 4000,
  npost = 4000,
  seed = NULL,
  verbose = TRUE,
  printevery = 1000,
  chain_index = 1
)

Arguments

X	A 3-D array of predictors with dimensions D × n × p.
Y	A matrix of outcomes with dimensions D × n.
intercept	Logical; include an intercept term? Default TRUE.
nburn	Integer; number of burn-in MCMC iterations. Default 4000.
npost	Integer; number of post-burn-in samples to retain. Default 4000.
seed	Integer or NULL; random seed for reproducibility. Default NULL.
verbose	Logical; print progress messages? Default TRUE.
printevery	Integer; print progress every this many iterations. Default 1000.
chain_index	Integer; index of this MCMC chain (for labeling prints). Default 1.

Value

A named list with components:

post_beta

Array npost × D × p of sampled regression coefficients.

post_alpha

Matrix npost × D of sampled intercepts (if used).

post_sigma2

Numeric vector of length npost, sampled residual variances.

post_lambda2

Matrix npost × p of local shrinkage parameters \lambda_j^2.

post_kappa

Matrix npost × p of auxiliary local hyperparameters \kappa_j.

post_tau2

Numeric vector of length npost, sampled global scale \tau^2.

post_eta

Numeric vector of length npost, sampled auxiliary global hyperparameter \eta.

post_fitted_Y

Array npost × D × n of posterior predictive draws (with noise).

post_pool_beta

Matrix (npost * D) × p of pooled coefficient draws.

post_pool_fitted_Y

Matrix (npost * D) × n of pooled predictive draws (with noise).

hat_matrix_proj

Matrix D × n × n of averaged projection hat-matrices. To avoid recalculate for estimating degree of freedom.

Examples

sim <- sim_B(n = 100, p = 20, type = "MAR", SNP = 1.5, corr = 0.5,
low_missing = TRUE, n_imp = 5, seed = 123)
X <- sim$data_MI$X
Y <- sim$data_MI$Y
fit <- horseshoe_mcmc(X, Y, nburn = 100, npost = 100)

BMIselect documentation built on Aug. 25, 2025, 5:11 p.m.