  Non-Bayesian social learning theory provides a framework that models
distributed inference for a group of agents interacting over a social network.
In this framework, each agent iteratively forms and communicates beliefs about
an unknown state of the world with their neighbors using a learning rule.
Existing approaches assume agents have access to precise statistical models (in
the form of likelihoods) for the state of the world. However in many
situations, such models must be learned from finite data. We propose a social
learning rule that takes into account uncertainty in the statistical models
using second-order probabilities. Therefore, beliefs derived from uncertain
models are sensitive to the amount of past evidence collected for each
hypothesis. We characterize how well the hypotheses can be tested on a social
network, as consistent or not with the state of the world. We explicitly show
the dependency of the generated beliefs with respect to the amount of prior
evidence. Moreover, as the amount of prior evidence goes to infinity, learning
occurs and is consistent with traditional social learning theory.
