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A loss-based prior for Gaussian graphical models

机译：基于高斯图形模型的亏损

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摘要

Gaussian graphical models play an important role in various areas such as genetics, finance, statistical physics and others. They are a powerful modelling tool, which allows one to describe the relationships among the variables of interest. From the Bayesian perspective, there are two sources of randomness: one is related to the multivariate distribution and the quantities that may parametrise the model, and the other has to do with the underlying graph, G, equivalent to describing the conditional independence structure of the model under consideration. In this paper, we propose a prior on G based on two loss components. One considers the loss in information one would incur in selecting the wrong graph, while the second penalises for large number of edges, favouring sparsity. We illustrate the prior on simulated data and on real datasets, and compare the results with other priors on G used in the literature. Moreover, we present a default choice of the prior as well as discuss how it can be calibrated so as to reflect available prior information.
机译：高斯图形模型在诸如遗传，金融，统计物理等的各种领域发挥着重要作用。它们是一个强大的建模工具，它允许人们描述感兴趣的变量之间的关系。从贝叶斯的角度来看，有两个随机性源：一个是与多变量分布和可能参数化模型的数量相关，另一个是与底层图，相当于描述条件独立结构的底层图。正在考虑的模型。在本文中，我们提出了基于两个损耗组件的G先前的G.一个人认为信息中的损失将在选择错误的图表时，而第二次惩罚大量边缘，有利于稀疏性。我们在模拟数据和实际数据集上说明了先前，并将结果与​​文献中使用的G上使用的其他前提进行比较。此外，我们介绍了先前的默认选择以及讨论如何校准它，以便反映可用的先前信息。

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