  Federated Learning (FL) involves training a model over a dataset distributed
among clients, with the constraint that each client's dataset is localized and
possibly heterogeneous. In FL, small and noisy datasets are common,
highlighting the need for well-calibrated models that represent the uncertainty
of predictions. The closest FL techniques to achieving such goals are the
Bayesian FL methods which collect parameter samples from local posteriors, and
aggregate them to approximate the global posterior. To improve scalability for
larger models, one common Bayesian approach is to approximate the global
predictive posterior by multiplying local predictive posteriors. In this work,
we demonstrate that this method gives systematically overconfident predictions,
and we remedy this by proposing $\beta$-Predictive Bayes, a Bayesian FL
algorithm that interpolates between a mixture and product of the predictive
posteriors, using a tunable parameter $\beta$. This parameter is tuned to
improve the global ensemble's calibration, before it is distilled to a single
model. Our method is evaluated on a variety of regression and classification
datasets to demonstrate its superiority in calibration to other baselines, even
as data heterogeneity increases. Code available at
https://github.com/hasanmohsin/betaPredBayesFL
