We consider a class of coloured graphical Gaussian models obtained by imposing equality constraints on the precision matrix in a Bayesian framework. The Bayesian prior for precision matrices is given by the coloured G-Wishart which is the Diaconis-Ylvisaker conjugate. In this paper, we develop a computationally efficient model search algorithm which combines linear regression with a double reversible jump Markov chain Monte Carlo. The latter is to estimate Bayes factors expressed as a posterior probabilities ratio of two competing models. We also establish the asymptotic consistency property of the model determination approach based on Bayes factors. Our procedure avoids an exhaustive search in the space of graphs, which is computationally impossible. Our method is illustrated with simulations and a real-world application with a protein signalling data set.

中文翻译：

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彩色图形高斯模型的贝叶斯模型选择方法

我们考虑通过在贝叶斯框架中对精度矩阵施加等式约束而获得的一类彩色图形高斯模型。精确矩阵的贝叶斯先验由彩色 G-Wishart 给出，它是 Diaconis-Ylvisaker 共轭。在本文中，我们开发了一种计算效率高的模型搜索算法，该算法将线性回归与双可逆跳跃马尔可夫链蒙特卡罗相结合。后者是估计贝叶斯因子，表示为两个竞争模型的后验概率比。我们还建立了基于贝叶斯因子的模型确定方法的渐近一致性属性。我们的程序避免在图空间中进行详尽的搜索，这在计算上是不可能的。