Convert an index covariance matrix to common-factor parameters
cov_to_factor.RdA multivariate normal index likelihood is supplied as a full covariance over
the observation vector, which cannot be drawn from one year at a time and does
not extend past the years it covers, so it is unusable for closed loop as
given. This decomposes it into a marginal scale and a single common factor,
obs_t = pred_t + d_t (lambda_t u + sqrt(1 - lambda_t^2) e_t), with
u shared across years and e_t independent. Both are then drawn
per year, and a projection year past the end of the covariance simply reuses
the mean loading and scale with the same u.