Distributed Bayesian learning with a Bernoulli model

In this paper, we study multi-agent systems where the agents learn not only from their own private observations, but also from the ones of other agents. We build on a recent work, where a Bayesian learning method proposed for a linear Gaussian model was studied. According to the method, the agents iteratively exchange information with their neighbors, and they update the summary of their information using the signals received from the neighbors. The agents aim at obtaining the global posterior distribution of the unknown parameters in as short time as possible in a distributed way. In this paper, the posteriors are modeled by Beta distributions. We address two settings, one where the private signals are observed without errors and another where they are contaminated with errors. Finally, we provide and discuss an example and show results from computer simulations.