Approximations and inference of dynamics on networks

The study of dynamics on networks is a subject area that has wide-reaching applications in areas such as epidemic outbreaks, rumour spreading, and innovation diffusion. In this thesis I look at how to both approximate and infer these dynamics. Specifically, I first explore mean-field approximations for SIS epidemic dynamics. I outline several established approximations of varying complexity, before investigating how their accuracy depends on the network and dynamical parameters. Next, I use a method called approximate lumping to coarse-grain SIS dynamics, and I show how this method allows us to derive mean-field approximations directly from the full master equation description, rather than via ad hoc moment closures, as is common. Finally, I consider inference of network dynamic parameters on multilayer networks. I focus on a case study of SIS dynamics occurring on a two-layer network, where the dynamics on one of the layers is unobserved or “hidden”. My goal is to estimate the SIS parameters, assuming I only have data about the events occurring on the visible layer. To do this I develop several simpler approximate models of the dynamics which have tractable likelihoods, and then use Markov chain Monte Carlo routines to infer the most likely parameters for these approximate dynamics.