  Bayesian Federated Learning (FL) has been recently introduced to provide
well-calibrated Machine Learning (ML) models quantifying the uncertainty of
their predictions. Despite their advantages compared to frequentist FL setups,
Bayesian FL tools implemented over decentralized networks are subject to high
communication costs due to the iterated exchange of local posterior
distributions among cooperating devices. Therefore, this paper proposes a
communication-efficient decentralized Bayesian FL policy to reduce the
communication overhead without sacrificing final learning accuracy and
calibration. The proposed method integrates compression policies and allows
devices to perform multiple optimization steps before sending the local
posterior distributions. We integrate the developed tool in an Industrial
Internet of Things (IIoT) use case where collaborating nodes equipped with
autonomous radar sensors are tasked to reliably localize human operators in a
workplace shared with robots. Numerical results show that the developed
approach obtains highly accurate yet well-calibrated ML models compatible with
the ones provided by conventional (uncompressed) Bayesian FL tools while
substantially decreasing the communication overhead (i.e., up to 99%).
Furthermore, the proposed approach is advantageous when compared with
state-of-the-art compressed frequentist FL setups in terms of calibration,
especially when the statistical distribution of the testing dataset changes.
