论文标题
测试后验预测差异的重要组成部分
Testing for the Important Components of Posterior Predictive Variance
论文作者
论文摘要
我们使用有限维离散随机变量的总方差和条件定律对后验预测方差进行分解。该随机变量总结了建模的各种特征，用于形成未来结果的预测。然后，我们测试该分解中的哪个术语足够小，不足以忽略。这使我们确定哪些离散随机变量对于预测间隔最重要。分解中的术语接受基于条件均值和方差的解释，并且类似于Cochran定理的平方误差定理分解中的术语，通常用于方差分析。因此，建模特征被视为完全随机设计的因素。在有多个分解的情况下，我们建议选择一种具有最佳预测覆盖范围的差异。
We give a decomposition of the posterior predictive variance using the law of total variance and conditioning on a finite dimensional discrete random variable. This random variable summarizes various features of modeling that are used to form the prediction for a future outcome. Then, we test which terms in this decomposition are small enough to ignore. This allows us identify which of the discrete random variables are most important to prediction intervals. The terms in the decomposition admit interpretations based on conditional means and variances and are analogous to the terms in a Cochran's theorem decomposition of squared error often used in analysis of variance. Thus, the modeling features are treated as factors in completely randomized design. In cases where there are multiple decompositions we suggest choosing the one that that gives the best predictive coverage with the smallest variance.
