Uncertainty quantification for White Matter Hyperintensity segmentation detects silent failures and improves automated Fazekas quantification

White Matter Hyperintensities (WMH) are key neuroradiological markers of small vessel disease present in brain MRI. Assessment of WMH is important in research and clinics. However, WMH are challenging to segment due to their high variability in shape, location, size, poorly defined borders, and similar intensity profile to other pathologies (e.g stroke lesions) and artefacts (e.g head motion). In this work, we assess the utility and semantic properties of the most effective techniques for uncertainty quantification (UQ) in segmentation for the WMH segmentation task across multiple test-time data distributions. We find UQ techniques reduce 'silent failure' by identifying in UQ maps small WMH clusters in the deep white matter that are unsegmented by the model. A combination of Stochastic Segmentation Networks with Deep Ensembles also yields the highest Dice and lowest Absolute Volume Difference % (AVD) score and can highlight areas where there is ambiguity between WMH and stroke lesions. We further demonstrate the downstream utility of UQ, proposing a novel method for classification of the clinical Fazekas score using spatial features extracted from voxelwise WMH probability and UQ maps. We show that incorporating WMH uncertainty information improves Fazekas classification performance and calibration. Our model with (UQ and spatial WMH features)/(spatial WMH features)/(WMH volume only) achieves a balanced accuracy score of 0.74/0.67/0.62, and root brier score of 0.65/0.72/0.74 in the Deep WMH and balanced accuracy of 0.74/0.73/0.71 and root brier score of 0.64/0.66/0.68 in the Periventricular region. We further demonstrate that stochastic UQ techniques with high sample diversity can improve the detection of poor quality segmentations.