  Individual-based models of contagious processes are useful for predicting
epidemic trajectories and informing intervention strategies. In such models,
the incorporation of contact network information can capture the non-randomness
and heterogeneity of realistic contact dynamics. In this paper, we consider
Bayesian inference on the spreading parameters of an SIR contagion on a known,
static network, where information regarding individual disease status is known
only from a series of tests (positive or negative disease status). When the
contagion model is complex or information such as infection and removal times
is missing, the posterior distribution can be difficult to sample from.
Previous work has considered the use of Approximate Bayesian Computation (ABC),
which allows for simulation-based Bayesian inference on complex models.
However, ABC methods usually require the user to select reasonable summary
statistics. Here, we consider an inference scheme based on the Mixture Density
Network compressed ABC (MDN-ABC), which minimizes the expected posterior
entropy in order to learn informative summary statistics. This allows us to
conduct Bayesian inference on the parameters of a partially observed contagious
process while also circumventing the need for manual summary statistic
selection. This methodology can be extended to incorporate additional
simulation complexities, including behavioral change after positive tests or
false test results.
