论文标题
测试平等和订单约束假设的野蛮豆键密度比的概括
A Generalization of the Savage-Dickey Density Ratio for Testing Equality and Order Constrained Hypotheses
论文作者
论文摘要
当对不受限制的替代方案测试精确（平等）假设时，野蛮的豆键密度比是贝叶斯因子的特定表达。该表达式大大简化了贝叶斯因子的计算，以假设在精确假设下的特定形式作为不受限制的先验的函数的成本。 Verdinelli和Wasserman（1995）提出了概括，以便可以在两个假设下自由指定先验，同时保持计算优势。当假设具有平等性以及对感兴趣参数的秩序约束时，本文介绍了这种概括的扩展。该方法用于使用JZS贝叶斯因子和多项式模型下的约束假设检验进行约束多变量t检验。
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 (1995) such that the priors can be freely specified under both hypotheses while keeping the computational advantage. This paper 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.
