Maximum-entropy moment-closure for stochastic systems on networks

TL;DR

This paper introduces a maximum-entropy approach to improve moment-closure methods for stochastic network models, addressing issues of non-uniqueness and inconsistency, and demonstrates its application to epidemic models with numerical experiments.

Contribution

It develops a maximum-entropy based moment-closure method that resolves non-uniqueness and inconsistency issues in stochastic network models.

Findings

The method effectively addresses non-uniqueness in moment-closure.

Numerical experiments demonstrate improved accuracy in epidemic modeling.

Sensitivity analysis highlights limitations of existing moment-closure techniques.

Abstract

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.