back_elbo: The Evidence lower bound.
In dcgerard/vicar: Various Ideas for Confounder Adjustment in Regression

The Evidence lower bound.

back_elbo(
  betahat_ols,
  S_diag,
  Amat,
  tau2_seq,
  pivec,
  lambda_seq,
  mubeta,
  mubeta_matrix,
  sig2beta_matrix,
  gamma_mat,
  muv,
  Sigma_v,
  phi,
  xi,
  var_inflate_pen = 0
)

`betahat_ols`	A vector of numerics. The ordinary least squares estimates of the regression coefficients.
`S_diag`	A vector of positive numerics. The standard errors of `betahat_ols`.
`Amat`	The A matrix for the variational EM.
`tau2_seq`	The known grid of prior mixing variances.
`pivec`	The current values of the mixing proportions.
`lambda_seq`	A vector of numerics greater than 1. The penalties on the pi's.
`mubeta`	The current means of the betas
`mubeta_matrix`	The current mixing means of the variational densities of the betas.
`sig2beta_matrix`	The current mixing variances of the variational densities of the betas.
`gamma_mat`	The current mixing proportions of the variational densities of the betas.
`muv`	A matrix of one column of numerics. The current mean of v.
`Sigma_v`	The current covariance matrix of the latent v.
`phi`	A numeric. The "g" hyperparameter.
`xi`	A positive numeric. The current value of xi.
`var_inflate_pen`	The penalty to apply on the variance inflation parameter. Defaults to 0, but should be something non-zero when `alpha = 1` and `scale_var = TRUE`.