多元高斯分布的部分随机优势
Partial stochastic dominance for the multivariate Gaussian distribution
摘要：
高斯比较不等式提供了一种方法，根据具有更简单相关结构的随机变量的概率来界定与多变量高斯随机向量相关的概率。本文建立了组内相关系数为正的多元正态随机向量的最大值的累积分布函数与标准正态随机变量的累积分布函数至多相交一次的部分随机优势结果。这一结果可以应用于贝叶斯设计的临床试验中，几个实验治疗相比，一个单一的控制。
英文摘要：
Gaussian comparison inequalities provide a way of bounding probabilities relating to multivariate Gaussian random vectors in terms of probabilities of random variables with simpler correlation structures. In this paper, we establish the partial stochastic dominance result that the cumulative distribution function of the maximum of a multivariate normal random vector, with positive intraclass correlation coefficient, intersects the cumulative distribution function of a standard normal random variable at most once. This result can be applied to the Bayesian design of a clinical trial in which several experimental treatments are compared to a single control.
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