A Unified Method for Checking Compatibility and Uniqueness for Finite Discrete Conditional Distributions |
| |
Authors: | Guo-liang Tian Ming Tan Kai Wang Ng Man-lai Tang |
| |
Institution: | 1. Department of Statistics and Actuarial Science , The University of Hong Kong , Hong Kong, P.R. China;2. Division of Biostatistics , University of Maryland Greenebaum Cancer Center , Baltimore, Maryland, USA gltian@hku.hk;4. Division of Biostatistics , University of Maryland Greenebaum Cancer Center , Baltimore, Maryland, USA;5. Department of Statistics and Actuarial Science , The University of Hong Kong , Hong Kong, P.R. China;6. Department of Mathematics , Hong Kong Baptist University , Hong Kong, P.R. China |
| |
Abstract: | 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. |
| |
Keywords: | Box constraints Compatibility Gibbs sampler Kullback–Leibler distance ?2-norm Quadratic optimization with constraints |
|
|