Po-Ling Lo, Unversity of Wisconsin-Madison

Estimation and inference for network contagion

We present two problems involving statistical inference and estimation for stochastic spreading over a fixed network. The first problem concerns hypothesis testing for the underlying graph over which the disease is spreading, when we only observe the infection states of individual nodes after a single epidemic outbreak. We present a permutation test that is valid under appropriate conditions on the homogeneity of the spreading parameters and assumptions regarding the symmetry groups of the graphs involved in the null and alternative hypotheses. The second problem concerns parameter estimation for a similar type of contagion model, which incorporates covariate information on each of the edges of the graph. In this setting, we assume the structure of the graph is known, and we also know the order in which nodes contract the disease from their infected neighbors. We derive consistency and asymptotic normality of the maximum likelihood estimator, which may be obtained via convex optimization.

This is joint work with Justin Khim (UPenn).