Decoding complex relationships among large numbers of variables with
relatively few observations is one of the crucial issues in science. One
approach to this problem is Gaussian graphical modeling, which describes
conditional independence of variables through the presence or absence of edges
in the underlying graph. In this paper, we introduce a novel and efficient
Bayesian framework for Gaussian graphical model determination which is a
trans-dimensional Markov Chain Monte Carlo (MCMC) approach based on a
continuous-time birth-death process. We cover the theory and computational
details of the method. It is easy to implement and computationally feasible for
high-dimensional graphs. We show our method outperforms alternative Bayesian
approaches in terms of convergence, mixing in the graph space and computing
time. Unlike frequentist approaches, it gives a principled and, in practice,
sensible approach for structure learning. We illustrate the efficiency of the
method on a broad range of simulated data. We then apply the method on
large-scale real applications from human and mammary gland gene expression
studies to show its empirical usefulness. In addition, we implemented the
method in the R package BDgraph which is freely available at
this http URL

本文介绍了一种基于贝叶斯框架的高斯图模型确定方法，它是基于连续时间出生 - 死亡过程的转维度马尔可夫链蒙特卡罗方法。该方法易于实现，在高维图形方面具有计算可行性，验证表明该方法在收敛、图形空间中的混合和计算时间方面优于替代贝叶斯方法，并应用于基因表达研究中。