brent_obj_norm: Objective function for updating variance inflation parameter...
In dcgerard/vicar: Various Ideas for Confounder Adjustment in Regression

Objective function for updating variance inflation parameter during EM for mixtures of normals prior.

1	brent_obj_norm(xi, qvals, S_diag, tau2_seq, resid_vec, var_inflate_pen = 0)

`xi`	The current value of the variance inflation parameter.
`qvals`	The probabilities from the E step. A matrix.
`S_diag`	A vector of positive numerics. The estimated standard errors.
`tau2_seq`	The grid of variances. This is the same thing as grid_seq in `mouthwash_second_step` if `likelihood = "normal"`.
`resid_vec`	The residuals from the OLS estimates and the bias term induced by the confounders.
`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`.