Bayesian Inference of Spreading Processes on Networks

Human susceptibility to epidemics of misinformation and disease has grown manyfold as the world we inhabit keeps getting smaller due to increased access to online information and soaring global mobility. Social media platforms have changed the way we consume information [Schmidt et al., 2017], and more and more people find their news through social media [Newman et al., 2015]. Following the 2016 presidential election in the United States, there have been investigations into the spread of false stories, or "fake news" on social media, and based on web browsing data, archives of fact-checking websites, and results from an online survey, a recent study found that social media were an important source of election news [Allcott and Gentzkow, 2017]. While ascertainment of social network structures is generally difficult using traditional survey-based approaches, such as name generators, which are survey questions designed to solicit information about friends and acquaintances of a subject, online platforms readily capture the structure of large-scale social networks, therefore making them well suited to study spread of information whether accurate or not. Further, although the transmission mechanisms are very different, the spread of information in online systems has many similarities to the spread of infectious diseases among hosts in a population. From a mathematical and statistical point of view, one can therefore investigate the spread of pathogens and the spread of information in the same framework as long as the network structure accurately captures the transmission pathways and the spreading process is parametrized appropriately. In this paper, we consider a simple susceptible-infected (SI) process and a more complex spreading process on a fixed and known network structure. This spreading process may be conceptualized as propagating either a pathogen or a piece of information. We focus on addressing two distinct questions that are relevant in both settings: (1) How to infer the unknown parameters associated with the spreading process?