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We study possible relations between the structure of the connectome, whitematter connecting different regions of brain, and Alzheimer disease. Regressionmodels in covariates including age, gender and disease status for the extent ofwhite matter connecting each pair of regions of brain are proposed. Subject Westudy possible relations between the Alzheimer's disease progression and thestructure of the connectome, white matter connecting different regions ofbrain. Regression models in covariates including age, gender and disease statusfor the extent of white matter connecting each pair of regions of brain areproposed. Subject inhomogeneity is also incorporated in the model throughrandom effects with an unknown distribution. As there are large number of pairsof regions, we also adopt a dimension reduction technique through graphon(Lovasz and Szegedy (2006)) functions, which reduces functions of pairs ofregions to functions of regions. The connecting graphon functions areconsidered unknown but assumed smoothness allows putting priors of lowcomplexity on them. We pursue a nonparametric Bayesian approach by assigning aDirichlet process scale mixture of zero mean normal prior on the distributionsof the random effects and finite random series of tensor products of B-splinespriors on the underlying graphon functions. Markov chain Monte Carlotechniques, for drawing samples for the posterior distributions are developed.The proposed Bayesian method overwhelmingly outperforms similar ANCOVA modelsin the simulation setup. The proposed Bayesian approach is applied on a datasetof 100 subjects and 83 brain regions and key regions implicated in the changingconnectome are identified.

Bayesian Modeling of the Structural Connectome for Studying Alzheimer Disease