bfa_gs_linked_gibbs: Fast Gibbs sampler for Bayesian factor analysis.
In dcgerard/vicar: Various Ideas for Confounder Adjustment in Regression

This is very similar to bfa_gd_gibbs except that we link the precisions of the observations with the precisions of the factors. For some reason, this works very well in practice.

bfa_gs_linked_gibbs(
  Linit,
  Finit,
  xi_init,
  phi_init,
  zeta_init,
  Y22init,
  Y21,
  Y31,
  Y32,
  nsamp,
  burnin,
  thin,
  rho_0,
  alpha_0,
  beta_0,
  eta_0,
  tau_0,
  display_progress
)

`Linit`	A numeric matrix. The initial values of the loadings.
`Finit`	A numeric matrix. The initial values for the factors.
`xi_init`	A numeric vector. The initial values of the precisions.
`phi_init`	A numeric scalar. The initial value of the mean of the precisions.
`zeta_init`	A numeric vector. The initial values of the augmented row precisions.
`Y22init`	A matrix of numerics. The initial value of Y22.
`Y21`	A matrix of numerics.
`Y31`	A matrix of numerics.
`Y32`	A matrix of numerics.
`nsamp`	The number of iterations to run in the Gibbs sampler, not including the burnin.
`burnin`	The number of iterations to burnin.
`thin`	We only collect samples every `thin` iterations.
`rho_0`	The prior sample size for column-specific the precisions.
`alpha_0`	The prior sample size for the mean of the column-specific precisions.
`beta_0`	The prior mean of the mean of the column-specific precisions.
`eta_0`	The prior sample size of the expanded parameters.
`tau_0`	The prior mean of of the expanded parameters.
`display_progress`	A logical. If `TRUE`, then a progress bar will be displayed and you'll be able to interrupt the C++ code. If `FALSE`, then neither of these capabilities will be provided.