gigg_fixed_gibbs_sampler {gigg}

Gibbs sampler for GIGG regression with fixed hyperparameters.

Description

An Rcpp function that implements a Gibbs sampler for GIGG regression with fixed hyperparameters.

Usage

gigg_fixed_gibbs_sampler(
  X,
  C,
  Y,
  grp_idx,
  grp_size,
  grp_size_cs,
  alpha_inits,
  beta_inits,
  lambda_sq_inits,
  gamma_sq_inits,
  eta_inits,
  p,
  q,
  tau_sq_init = 1,
  sigma_sq_init = 1,
  nu_init = 1,
  n_burn_in = 500L,
  n_samples = 1000L,
  n_thin = 1L,
  stable_const = 1e-07,
  verbose = TRUE,
  btrick = FALSE,
  stable_solve = FALSE
)

Arguments

X

A (n x M) matrix of covariates that we want to apply GIGG shrinkage on.

C

A (n x K) matrix of covariates that we want to apply no shrinkage on (typically intercept + adjustment covariates).

Y

A (n x 1) column vector of responses.

grp_idx

A (1 x M) row vector indicating which group of the J groups the M covariates in X belong to.

grp_size

A (1 x J) row vector indicating the number of covariates in each group.

grp_size_cs

A (1 x J) row vector that is the cumulative sum of grp_size (indicating the indicies where each group ends).

alpha_inits

A (K x 1) column vector containing initial values for the regression coefficients corresponding to C.

beta_inits

A (M x 1) column vector containing initial values for the regression coefficients corresponding to X.

lambda_sq_inits

A (M x 1) column vector containing initial values for the local shrinkage parameters.

gamma_sq_inits

A (J x 1) column vector containing initial values for the group shrinkage parameters.

eta_inits

A (J x 1) column vector containing initial values for the mixing parameters.

p

A (J x 1) column vector of shape parameter for the prior on the group shrinkage parameters.

q

A (J x 1) column vector of shape parameter for the prior on the individual shrinkage parameters.

tau_sq_init

Initial value for the global shrinkage parameter (double).

sigma_sq_init

Initial value for the residual variance (double).

nu_init

Initial value for the augmentation variable (double).

n_burn_in

The number of burn-in samples (integer).

n_samples

The number of posterior draws (integer).

n_thin

The thinning interval (integer).

stable_const

Parameter that controls numerical stability of the algorithm (double).

verbose

Boolean value which indicates whether or not to print the progress of the Gibbs sampler.

btrick

Boolean value which indicates whether or not to use the computational trick in Bhattacharya et al. (2016). Only recommended if number of covariates is much larger than the number of observations.

stable_solve

default to FALSE

Value

A list containing the posterior draws of (1) the regression coefficients (alphas and betas) (2) the individual shrinkage parameters (lambda_sqs) (3) the group shrinkage parameters (gamma_sqs) (4) the global shrinkage parameter (tau_sqs) and (5) the residual error variance (sigma_sqs). The list also contains details regarding the dataset (X, C, Y, grp_idx) and Gibbs sampler details (n_burn_in, n_samples, and n_thin).