  This work demonstrates the ability to produce readily interpretable
statistical metrics for model fit, fixed effects covariance coefficients, and
prediction confidence. Importantly, this work compares 4 suitable and commonly
applied epistemic UQ approaches, BNN, SWAG, MC dropout, and ensemble approaches
in their ability to calculate these statistical metrics for the ARMED MEDL
models. In our experiment for AD prognosis, not only do the UQ methods provide
these benefits, but several UQ methods maintain the high performance of the
original ARMED method, some even provide a modest (but not statistically
significant) performance improvement. The ensemble models, especially the
ensemble method with a 90% subsampling, performed well across all metrics we
tested with (1) high performance that was comparable to the non-UQ ARMED model,
(2) properly deweights the confounds probes and assigns them statistically
insignificant p-values, (3) attains relatively high calibration of the output
prediction confidence. Based on the results, the ensemble approaches,
especially with a subsampling of 90%, provided the best all-round performance
for prediction and uncertainty estimation, and achieved our goals to provide
statistical significance for model fit, statistical significance covariate
coefficients, and confidence in prediction, while maintaining the baseline
performance of MEDL using ARMED
