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Primary Submission Category: Causal Inference in Networks

Bayesian inference for causal effects under interference in the presence of a partially observed diffusion process on networks

Authors: Fei Fang, Amir Ghasemian, Laura Forastiere, Edo Airoldi,

Presenting Author: Fei Fang*

Behaviors are likely to spread in a connected population and the presence of a behavioral intervention may boost this spread. We consider the setting where we observe at baseline the set of treated units, and at baseline and follow-up the social network and the prevalence of behaviors. To investigate the problem, we assume a network-based diffusion models, including network susceptible-infected-susceptible (SIS) model and network susceptible-infected (SI) model, formulated as a continuous-time Markov process. We develop a Bayesian data augmentation procedure to impute over time the behavioral change as a result of diffusion from social ties or as a result of the intervention for the treated. We also extend this procedure to a setting where the network also evolves. Based on the estimated parameters, we use an imputation method to evaluate the causal effects of hypothetical treatment allocations, with different rates and network-based strategies. Under simplified network models, we also derived closed forms for the expected effect of increasing the treatment rate under different baseline behavior prevalence and network structures. We apply the proposed method to a factorial randomized experiment delivering a behavioral intervention in villages in Honduras under different treatment rates and strategies. This data allows us to compare adoption rates under a hypothetical strategy imputed in one arm with the actual adoption rates observed in the arm assigned to that strategy.