  Statistical shape modeling (SSM) enables population-based quantitative
analysis of anatomical shapes, informing clinical diagnosis. Deep learning
approaches predict correspondence-based SSM directly from unsegmented 3D images
but require calibrated uncertainty quantification, motivating Bayesian
formulations. Variational information bottleneck DeepSSM (VIB-DeepSSM) is an
effective, principled framework for predicting probabilistic shapes of anatomy
from images with aleatoric uncertainty quantification. However, VIB is only
half-Bayesian and lacks epistemic uncertainty inference. We derive a fully
Bayesian VIB formulation and demonstrate the efficacy of two scalable
implementation approaches: concrete dropout and batch ensemble. Additionally,
we introduce a novel combination of the two that further enhances uncertainty
calibration via multimodal marginalization. Experiments on synthetic shapes and
left atrium data demonstrate that the fully Bayesian VIB network predicts SSM
from images with improved uncertainty reasoning without sacrificing accuracy.
