Circular prediction regions for miss distance models under heteroskedasticity

Abstract

AbstractCircular prediction regions are used in ballistic testing to express the uncertainty in shot accuracy. We compare two modeling approaches for estimating circular prediction regions for the miss distance of a ballistic projectile. The miss distance response variable is bivariate normal and has a mean and variance that can change with one or more experimental factors. The first approach fits a heteroskedastic linear model using restricted maximum likelihood, and uses the Kenward‐Roger statistic to estimate circular prediction regions. The second approach fits an analogous Bayesian model with unrestricted likelihood modifications, and computes circular prediction regions by sampling from the posterior predictive distribution. The two approaches are applied to an example problem, and are compared using simulation.