BMIselect (version 1.0.1)

spike_laplace_partially_mcmc: Spike-and-Laplace MCMC Sampler for Multiply-Imputed Regression

Description

Implements Bayesian variable selection using a spike-and-slab prior with a Laplace (double-exponential) slab on nonzero coefficients. Latent inclusion indicators gamma follow Bernoulli(theta), and their probabilities follow independent Beta(a, b) priors.

Usage

spike_laplace_partially_mcmc(
  X,
  Y,
  intercept = TRUE,
  a = 2,
  b = NULL,
  nburn = 4000,
  npost = 4000,
  seed = NULL,
  verbose = TRUE,
  printevery = 1000,
  chain_index = 1
)

Value

A named list with components:

post_rho

Numeric vector length npost, sampled global scale \(\rho\).

post_gamma

Matrix npost * p of sampled inclusion indicators.

post_theta

Matrix npost * p of sampled Beta parameters \(\theta_j\).

post_alpha

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

post_lambda2

Matrix npost * p of sampled local scale parameters \(\lambda_j^2\).

post_sigma2

Numeric vector length npost, sampled residual variances.

post_beta

Array npost * D * p of sampled regression coefficients.

post_fitted_Y

Array npost * D * n of posterior predictive draws (including 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.

a, b

Numeric values of the rho hyperparameters used.

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.

a

Numeric; shape parameter of the Gamma prior. Default 2.

b

Numeric or NULL; scale parameter of the Gamma prior. If NULL, defaults to 0.5*(D+1)/(D*(a-1)).

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 messages). Default 1.

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 <- spike_laplace_partially_mcmc(X, Y, nburn = 10, npost = 10)