
Bayesian Factor Analysis Based on Concen tration 191
Suppo se then that we have s e lec ted the factor model with q factors. This
says that the true corr e lation matrix satisfies (9.3) and we must estimate R
so that our estimate is in H
q
0
. Naturally we want to maximize the relative
belief ratio RB(R) for R ∈H
q
0
but this is computationally difficult as the s e t
is not convex. Note that this also rules out using the co nditiona l expectation
given that R ∈ H
q
0
, as we are not guaranteed that this value is in H
q
0
. We
can, however, use the following approximation. Let
ˆ
R denote the plug-in MLE
of R, i.e., the estimate obtained from the MLE of Σ given by (