Accurate, automated white matter hyperintensity (WMH) segmentations are needed for large-scale studies to understand contributions of WMH to neurological diseases. We evaluated Bayesian Model Selection (BaMoS), a hierarchical fully-unsupervised model selection framework for WMH segmentation. We compared BaMoS segmentations to semi-automated segmentations, and assessed whether they predicted longitudinal cognitive change in control, early Mild Cognitive Impairment (EMCI), late Mild Cognitive Impairment (LMCI), subjective/significant memory concern (SMC) and Alzheimer's (AD) participants. Data were downloaded from the Alzheimer's disease Neuroimaging Initiative (ADNI). Magnetic resonance images from 30 control and 30 AD participants were selected to incorporate multiple scanners, and were semi-automatically segmented by 4 raters and BaMoS. Segmentations were assessed using volume correlation, Dice score, and other spatial metrics. Linear mixed-effect models were fitted to 180 control, 107 SMC, 320 EMCI, 171 LMCI and 151 AD participants separately in each group, with the outcomes being cognitive change (e.g. mini-mental state examination; MMSE), and BaMoS WMH, age, sex, race and education used as predictors. There was a high level of agreement between BaMoS' WMH segmentation volumes and a consensus of rater segmentations, with a median Dice score of 0.74 and correlation coefficient of 0.96. BaMoS WMH predicted cognitive change in: control, EMCI, and SMC groups using MMSE; LMCI using clinical dementia rating scale; and EMCI using Alzheimer's disease assessment scale-cognitive subscale (p < 0.05, all tests). BaMoS compares well to semi-automated segmentation, is robust to different WMH loads and scanners, and can generate volumes which predict decline. BaMoS can be applicable to further large-scale studies.