  Non-Bayesian social learning theory provides a framework for distributed
inference of a group of agents interacting over a social network by
sequentially communicating and updating beliefs about the unknown state of the
world through likelihood updates from their observations. Typically, likelihood
models are assumed known precisely. However, in many situations the models are
generated from sparse training data due to lack of data availability, high cost
of collection/calibration, limits within the communications network, and/or the
high dynamics of the operational environment. Recently, social learning theory
was extended to handle those model uncertainties for categorical models. In
this paper, we introduce the theory of Gaussian uncertain models and study the
properties of the beliefs generated by the network of agents. We show that even
with finite amounts of training data, non-Bayesian social learning can be
achieved and all agents in the network will converge to a consensus belief that
provably identifies the best estimate for the state of the world given the set
of prior information.
