论文标题
彩色图形高斯模型的贝叶斯模型选择方法
Bayesian model selection approach for colored graphical Gaussian models
论文作者
论文摘要
我们考虑通过在贝叶斯框架中将对称性约束放在精确矩阵上获得的一类彩色图形高斯模型。精确矩阵上的先前分布是彩色$ g $ -wishart，这是diaconis-ylvisaker con轭的先验。在本文中，我们开发了一种计算高效的模型搜索算法，该算法将线性回归与双重可逆跳跃马尔可夫链蒙特卡洛（MCMC）方法相结合。后者是为了估计以两个竞争模型的后验概率比例表示的贝叶斯因子。我们还基于贝叶斯因素建立了模型选择程序的渐近一致性。我们的过程避免了详尽的搜索，这在计算上是不可能的。使用仿真和带有蛋白质信号数据集的现实应用程序来说明我们的方法。
We consider a class of colored graphical Gaussian models obtained by placing symmetry constraints on the precision matrix in a Bayesian framework. The prior distribution on the precision matrix is the colored $G$-Wishart prior which is the Diaconis-Ylvisaker conjugate prior. In this paper, we develop a computationally efficient model search algorithm which combines linear regression with a double reversible jump Markov chain Monte Carlo (MCMC) method. The latter is to estimate the Bayes factors expressed as the ratio of posterior probabilities of two competing models. We also establish the asymptotic consistency property of the model selection procedure based on the Bayes factors. Our procedure avoids an exhaustive search which is computationally impossible. Our method is illustrated with simulations and a real-world application with a protein signalling data set.
