  Bayesian Federated Learning (FL) offers a principled framework to account for
the uncertainty caused by limitations in the data available at the nodes
implementing collaborative training. In Bayesian FL, nodes exchange information
about local posterior distributions over the model parameters space. This paper
focuses on Bayesian FL implemented in a device-to-device (D2D) network via
Decentralized Stochastic Gradient Langevin Dynamics (DSGLD), a recently
introduced gradient-based Markov Chain Monte Carlo (MCMC) method. Based on the
observation that DSGLD applies random Gaussian perturbations of model
parameters, we propose to leverage channel noise on the D2D links as a
mechanism for MCMC sampling. The proposed approach is compared against a
conventional implementation of frequentist FL based on compression and digital
transmission, highlighting advantages and limitations.
