Questions from Yanghyeon Cho

[pcarbo]

Some comments from Yanghyeon Cho that we need to address with either (i) fixes to the code or (ii) more clearly
documented interface. Note that these are comments about the mr.ash.alpha package, but we want to make sure
they are addressed in this package.

My understanding is that the mr.ash algorithm updates the scaled quantities (e.g., βj/σ) iteratively until convergence,
and then one would typically rescale back to the original scale after the loop. However, when I look at the implementation
(e.g., lines 315–317 in mr.ash.R), it seems that the rescaling is only performed under specific conditions, rather than always.

This leads to a couple of questions:

Why is the rescaling back to the original scale only done in certain cases, rather than unconditionally after the loop?
Relatedly, is method_q = "sigma_scaled_beta" intended to be a valid option? From the code, it looks like method_q
is currently limited to > c("sigma_dep_q", "sigma_indep_q").

More generally, what is the rationale for not always
reverting to the original (unscaled) parameterization at the end of the updates?