ABSTRACT

The Savage–Dickey density ratio is a specific expression of the Bayes factor when testing a precise (equality constrained) hypothesis against an unrestricted alternative. The expression greatly simplifies the computation of the Bayes factor at the cost of assuming a specific form of the prior under the precise hypothesis as a function of the unrestricted prior. A generalization was proposed by Verdinelli and Wasserman such that the priors can be freely specified under both hypotheses while keeping the computational advantage. This article presents an extension of this generalization when the hypothesis has equality as well as order constraints on the parameters of interest. The methodology is used for a constrained multivariate t-test using the JZS Bayes factor and a constrained hypothesis test under the multinomial model.

摘要

Savage-Dickey 密度比是贝叶斯因子在针对不受限制的替代方案测试精确（平等约束）假设时的特定表达。该表达式极大地简化了贝叶斯因子的计算，代价是在精确假设下假设特定形式的先验作为无限制先验的函数。Verdinelli 和 Wasserman 提出了一种概括，使得可以在两个假设下自由指定先验，同时保持计算优势。当假设对感兴趣的参数具有相等性和顺序约束时，本文介绍了这种概括的扩展。该方法用于受约束的多变量t- 使用 JZS 贝叶斯因子和多项模型下的约束假设检验进行检验。