Circular 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.

中文翻译：

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异方差下缺失距离模型的圆形预测区域

圆形预测区域用于弹道测试以表达射击精度的不确定性。我们比较了两种用于估计弹道弹丸未命中距离的圆形预测区域的建模方法。未命中距离响应变量是二元正态变量，其均值和方差可随一个或多个实验因素而变化。第一种方法使用受限最大似然拟合异方差线性模型，并使用 Kenward-Roger 统计量来估计圆形预测区域。第二种方法拟合具有无限制似然修改的类似贝叶斯模型，并通过从后验预测分布中采样来计算圆形预测区域。将这两种方法应用于示例问题，并使用仿真进行比较。