正态分层模型中超先验的后验性质和容许性
Posterior propriety and admissibility of hyperpriors in normal hierarchical models
摘要：
分层建模是美妙的，并在这里停留，但超参数先验往往是在一个休闲的方式选择。不幸的是，随着超参数数量的增加，随意选择的影响会成倍增加，导致性能大幅下降。作为一个极端但并不罕见的例子，使用错误的超参数先验甚至会导致不恰当的后验。对于可交换的层次多元正态模型，我们首先确定当一个标准类的层次先验结果在适当或不适当的后验。接下来，我们确定这类元素导致二次损失下的平均值的可接受估计，这样的考虑提供了一个有用的指导方针，分层先验之间的选择。最后，计算问题与所得的后验分布得到解决。
英文摘要：
Hierarchical modeling is wonderful and here to stay, but hyperparameter priors are often chosen in a casual fashion. Unfortunately, as the number of hyperparameters grows, the effects of casual choices can multiply, leading to considerably inferior performance. As an extreme, but not uncommon, example use of the wrong hyperparameter priors can even lead to impropriety of the posterior. For exchangeable hierarchical multivariate normal models, we first determine when a standard class of hierarchical priors results in proper or improper posteriors. We next determine which elements of this class lead to admissible estimators of the mean under quadratic loss; such considerations provide one useful guideline for choice among hierarchical priors. Finally, computational issues with the resulting posterior distributions are addressed.
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