uniform_mix_llike: Log-likelihood when using t errors and mixture of uniforms...
In dcgerard/vicar: Various Ideas for Confounder Adjustment in Regression

Log-likelihood when using t errors and mixture of uniforms prior.

uniform_mix_llike(
  pi_vals,
  z2,
  xi,
  betahat_ols,
  S_diag,
  alpha_tilde,
  a_seq,
  b_seq,
  lambda_seq,
  degrees_freedom,
  var_inflate_pen = 0
)

`pi_vals`	A vector of non-negative numerics that sums to one. The current values of the mixing proportions.
`z2`	A vector of numerics. The current values of the unobserved confounders.
`xi`	A positive numeric. The current value of the variance inflation factor.
`betahat_ols`	A vector of numerics. The OLS regression coefficients.
`S_diag`	A vector of positive numerics. The standard errors.
`alpha_tilde`	A matrix of numerics. The estimates of the coefficients of the confounders.
`a_seq`	A vector of numerics (usually non-positive). The lower bounds of the uniform mixing densities.
`b_seq`	A vector of numerics (usually non-negative). The upper bounds of the uniform mixing densities.
`lambda_seq`	A vector of numerics greater than 1. The penalties on the mixing proportions.
`degrees_freedom`	A positive scalar or a vector of positive scalars the length of `betahat_ols`. The degrees of freedom of the t-distribution.
`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`.