B1609
Title: Bayesian lesion estimation with a structured spike-and-slab prior
Authors: Habib Ganjgahi - Statistics Department, University of Oxford (United Kingdom) [presenting]
Anna Menacher - University of Oxford (United Kingdom)
Chris Holmes - University of Oxford (United Kingdom)
Thomas Nichols - University of Oxford (United Kingdom)
Abstract: Neural demyelination and damages to the human brain nervous system appear at hyperintense areas in magnetic resonance imaging (MRI) scans, known as lesions. Modelling binary images at the population level, where each voxel represents the existence of a lesion, plays an important role in understanding ageing and inflammatory diseases. Current approaches either fit a logistic regression independently to each voxel ignoring any form of spatial dependence or are Bayesian accounting for shared information between neighbouring voxels. However, Bayesian spatial models rely on computationally intensive Markov Chain Monte Carlo (MCMC) methods for inference which are not feasible for large-scale studies. We propose a scalable hierarchical Bayesian spatial model 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/exclusion. We use Bayesian Bootstrap for inference accompanied by stochastic variational inference that allows our method to scale to large sample sizes. Moreover, we identify promising sparse high-probability subsets by performing dynamic posterior exploration for structured spike-and-slab regression through approximation of the posterior marginal of latent active variables. Lastly, we validate our results via simulation studies and an application to the UK Biobank.
