  Neural demyelination and brain damage accumulated in white matter appear as
hyperintense areas on T2-weighted MRI scans in the form of lesions. Modeling
binary images at the population level, where each voxel represents the
existence of a lesion, plays an important role in understanding aging and
inflammatory diseases. We propose a scalable hierarchical Bayesian spatial
model, called BLESS, capable of handling binary responses by placing continuous
spike-and-slab mixture priors on spatially-varying parameters and enforcing
spatial dependency on the parameter dictating the amount of sparsity within the
probability of inclusion. The use of mean-field variational inference with
dynamic posterior exploration, which is an annealing-like strategy that
improves optimization, allows our method to scale to large sample sizes. Our
method also accounts for underestimation of posterior variance due to
variational inference by providing an approximate posterior sampling approach
based on Bayesian bootstrap ideas and spike-and-slab priors with random
shrinkage targets. Besides accurate uncertainty quantification, this approach
is capable of producing novel cluster size based imaging statistics, such as
credible intervals of cluster size, and measures of reliability of cluster
occurrence. Lastly, we validate our results via simulation studies and an
application to the UK Biobank, a large-scale lesion mapping study with a sample
size of 40,000 subjects.
