  As societies around the world are ageing, the number of Alzheimer's disease
(AD) patients is rapidly increasing. To date, no low-cost, non-invasive
biomarkers have been established to advance the objectivization of AD diagnosis
and progression assessment. Here, we utilize Bayesian neural networks to
develop a multivariate predictor for AD severity using a wide range of
quantitative EEG (QEEG) markers. The Bayesian treatment of neural networks both
automatically controls model complexity and provides a predictive distribution
over the target function, giving uncertainty bounds for our regression task. It
is therefore well suited to clinical neuroscience, where data sets are
typically sparse and practitioners require a precise assessment of the
predictive uncertainty. We use data of one of the largest prospective AD EEG
trials ever conducted to demonstrate the potential of Bayesian deep learning in
this domain, while comparing two distinct Bayesian neural network approaches,
i.e., Monte Carlo dropout and Hamiltonian Monte Carlo.
