A Unified Method for Checking Compatibility and Uniqueness for Finite Discrete Conditional Distributions
A Unified Method for Checking Compatibility and Uniqueness for Finite Discrete Conditional Distributions
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DOI：
10.1080/03610920802169586
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发表时间：
2009-01-01
影响因子：
0.8
通讯作者：
Tang, Man-Lai
中科院分区：
文献类型：
--
作者：
Tian, Guo-Liang;Tan, Ming;Tang, Man-Lai
检查两个给定条件分布的兼容性并识别相应的唯一兼容边缘分布是数理统计中的重要问题，特别是在贝叶斯推理中。在本文中，我们开发了一种统一的方法来检查两个有限离散条件分布的兼容性和唯一性。通过将兼容性问题表述为受约束的线性方程组，可以将其简化为具有框约束的二次优化问题。我们还将所提出的方法从二维情况扩展到更高维的情况。最后，我们表明我们的方法可以轻松应用于检查回归函数和条件分布的兼容性和唯一性。使用几个数值例子来说明所提出的方法。还提供了与现有方法的一些比较。
Checking compatibility for two given conditional distributions and identifying the corresponding unique compatible marginal distributions are important problems in mathematical statistics, especially in Bayesian inferences. In this article, we develop a unified method to check the compatibility and uniqueness for two finite discrete conditional distributions. By formulating the compatibility problem into a system of linear equations subject to constraints, it can be reduced to a quadratic optimization problem with box constraints. We also extend the proposed method from two-dimensional cases to higher-dimensional cases. Finally, we show that our method can be easily applied to checking compatibility and uniqueness for a regression function and a conditional distribution. Several numerical examples are used to illustrate the proposed method. Some comparisons with existing methods are also presented.