This paper addresses the problem of information consensus in a team of networked agents by presenting a generic consensus method that permits agreement to a Bayesian fusion of uncertain local parameter estimates. In particular, the method utilizes the concept of conjugacy of probability distributions to achieve a steady-state estimate consistent with a Bayesian combination of each agent's local knowledge, without requiring complex channel filters or being limited to normally distributed uncertainties. It is shown that this algorithm, termed hyperparameter consensus, is adaptable to many local uncertainty distributions within the exponential family, and will converge to a Bayesian fusion of local estimates with some standard assumptions on the network topology. (C) 2011 Elsevier Ltd. All rights reserved.