The Role of Prior Information in Inference on the Annualized Rates of Mass Shootings in the United States

Abstract

While public debate over gun control in the United States has often hinged on individual public mass shooting incidents, legislative action should be informed by knowledge of the long-term evolution of these events. We present a new Bayesian model for the annualized rate of public mass shootings in the United States based on a Gaussian process with a time-varying mean function. While we present specific findings on long- and short-term trends of these shootings in the U.S., our focus is on understanding the role of model design and prior information in policy analysis. Using a Markov chain Monte Carlo inference technique, we explore the posterior consequences of different prior choices and explore correlations between hyperparameters. We demonstrate that the findings about the long-term evolution of the annualized rate of public mass shootings are robust to choices about prior information, while inferences about the timescale and amplitude of short-term variation depend sensitively on the prior. This work addresses the policy implications of implicit and explicit choices of prior information in model design and the utility of full Bayesian inference in evaluating the consequences of those choices.