Here, we investigate whether (and how) experimental design could aid in the estimation of the precision matrix in a Gaussian chain graph model, especially the interplay between the design, the effect of the experiment and prior knowledge about the effect. Estimation of the precision matrix is a fundamental task to infer biological graphical structures like microbial networks. We compare the marginal posterior precision of the precision matrix under four priors: flat, conjugate Normal-Wishart, Normal-MGIG and a general independent. Under the flat and conjugate priors, the Laplace-approximated posterior precision is not a function of the design matrix rendering useless any efforts to find an optimal experimental design to infer the precision matrix. In contrast, the Normal-MGIG and general independent priors do allow for the search of optimal experimental designs, yet there is a sharp upper bound on the information that can be extracted from a given experiment. We confirm our theoretical findings via a simulation study comparing i) the KL divergence between prior and posterior and ii) the Stein's loss difference of MAPs between random and no experiment. Our findings provide practical advice for domain scientists conducting experiments to better infer the precision matrix as a representation of a biological network.
翻译:在此,我们调查实验设计是否(以及如何)有助于估计高斯链图模型中精确矩阵的精确度,特别是设计、实验效果和先前对效果的了解之间的相互作用。精确矩阵的估算是推断微生物网络等生物图形结构的一项基本任务。我们比较了精确矩阵在四个前几个前几个前四个前的边际后端精确度:平坦、共和正常-Wishart、正常-GGIG和一般独立。在平坦和共和前两个前科中,Laplace-相近后部精确度并不是设计矩阵的功能,它使得寻找最佳实验设计以推断精确度矩阵的任何努力毫无用处。相比之下,正常-MGIG和一般独立前几个前的精确度确实允许搜索最佳实验设计,但从特定实验中提取的信息却有一个尖锐的上层。我们通过模拟研究证实了我们的理论结论,比较了i)KL先前和后两个后半部之间的差异和二)斯坦因MAP在随机和无实验之间的损失差异。我们的研究结果显示生物领域科学家网络的精确性比较为进行更精确性提供了实际的模型。