The New England Journal of Statistics in Data Science

Social networks primarily focus on the phenomenon of the contagion effect when examining behavior patterns within specific social groups. However, the impact of peer effects is characterized by the tendency to imitate the behaviors of friends and the selection process, where individuals tend to affiliate with others sharing similar traits, significantly contributing to shaping social behaviors that are frequently interconnecting. This article presents a Bayesian approach that uses latent-space estimation methods to detect and examine contagion effects, considering the impact of social selection. The research provides a methodological explanation, followed by a sequence of simulation trials designed to explore operational functionalities and possible real-world applications. To illustrate the potential correlation between changes in alcohol use and the influence of social networks, this study concludes by presenting an example of adolescent drinking behavior.

Double generalized linear models provide a flexible framework for modeling data by allowing the mean and the dispersion to vary across observations. Common members of the exponential dispersion family including the Gaussian, Poisson, compound Poisson-gamma (CP-g), Gamma and inverse-Gaussian are known to admit such models. The lack of their use can be attributed to ambiguities that exist in model specification under a large number of covariates and complications that arise when data display complex spatial dependence. In this work we consider a hierarchical specification for the CP-g model with a spatial random effect. The spatial effect is targeted at performing uncertainty quantification by modeling dependence within the data arising from location based indexing of the response. We focus on a Gaussian process specification for the spatial effect. Simultaneously, we tackle the problem of model specification for such models using Bayesian variable selection. It is effected through a continuous spike and slab prior on the model parameters, specifically the fixed effects. The novelty of our contribution lies in the Bayesian frameworks developed for such models. We perform various synthetic experiments to showcase the accuracy of our frameworks. They are then applied to analyze automobile insurance premiums in Connecticut, for the year of 2008.