Modeling the time evolution of the annualized rate of public mass shootings with Gaussian processes

Much of the public policy debate over gun control and gun rights in the United States hinges on the alarming incidence of public mass shootings, here defined as attacks killing four or more victims. Several times in recent years, individual, highly salient public mass shooting incidents have galvanized public discussion of reform efforts. But deliberative legislative action proceeds over a much longer timescale that should be informed by knowledge of the long term evolution of these events. We have used Stan to develop a new model for the annualized rate of public mass shootings in the United States based on a Gaussian process with a time-varying mean function. This design yields a predictive model with the full non-parametric flexibility of a Gaussian process, while retaining the direct interpretability of a parametric model for long-term evolution of the mass shooting rate. We apply this model to the Mother Jones database of public mass shootings and explore the posterior consequences of different prior choices and of correlations between hyperparameters. We reach conclusions about the long term evolution of the rate of public mass shootings in the United States and short-term periods deviating from this trend.