We show that the only parameter prior for complete Gaussian DAG models that satisfies global parameter independence, complete model equivalence, and some weak regularity assumptions, is the normal-Wishart distribution. Our analysis is based on the following new characterization of the Wishart distribution: let W be an n x n, n >= 3, positive-definite symmetric matrix of random variables and f(W) be a pdf of W. Then, f(W) is a Wishart distribution if and only if W_{11}-W_{12}W_{22}^{-1}W_{12}' is independent of {W_{12}, W_{22}} for every block partitioning W_{11}, W_{12}, W_{12}', W_{22} of W. Similar characterizations of the normal and normal-Wishart distributions are provided as well. We also show how to construct a prior for every DAG model over X from the prior of a single regression model.
翻译：我们显示,完整高西亚 DAG 模型之前唯一符合全球参数独立性、完全模型等同性以及某些常规性差假设的参数是正常Wishart分布。我们的分析基于Wishart分布的以下新特征:W必须是随机变量和f(W)的正-确定对称矩阵的n x n, n ⁇ 3, 随机变量和f(W) 的正-确定对称矩阵的pdf。 然后, f(W) 是Wishart分布, 前提是W*11}-WQQQ12}W ⁇ 22 ⁇ -1W*12}'独立于W*12}, W ⁇ 22 ⁇ 用于W*11}、W*12}、W*12}的每个区块分割的 W*12}、W*12}、W*12}、W ⁇ 22}。正常和正常-Wishart分布的类似特征也提供了。我们还演示了如何为X以上每个DAG模型从以前的单一回归模型建立前的前置前置前置。
相关内容
微信扫码咨询专知VIP会员