  Moment-closure methods are popular tools to simplify the mathematical
analysis of stochastic models defined on networks, in which high dimensional
joint distributions are approximated (often by some heuristic argument) as
functions of lower dimensional distributions. Whilst undoubtedly useful,
several such methods suffer from issues of non-uniqueness and inconsistency.
These problems are solved by an approach based on the maximisation of entropy,
which is motivated, derived and implemented in this article. A series of
numerical experiments are also presented, detailing the application of the
method to the Susceptible-Infective-Recovered model of epidemics, as well as
cautionary examples showing the sensitivity of moment-closure techniques in
general.
