Directional tests to compare incomplete undirected graphs are developed in the general context of covariance selection for Gaussian graphical models. The exactness of the underlying saddlepoint approximation is proved for chordal graphs and leads to exact control of the size of the tests, given that the only approximation error involved is due to the numerical calculation of two scalar integrals. Although exactness is not guaranteed for non-chordal graphs, the ability of the saddlepoint approximation to control the relative error leads the directional test to overperform its competitors even in these cases. The accuracy of our proposal is verified by simulation experiments under challenging scenarios, where inference via standard asymptotic approximations to the likelihood ratio test and some of its higher-order modifications fails. The directional approach is used to illustrate the assessment of Markovian dependencies in a dataset from a veterinary trial on cattle. A second example with microarray data shows how to select the graph structure related to genetic anomalies due to acute lymphocytic leukemia.

翻译：在协方差选择的广义高斯图模型框架下，我们发展了用于比较非完备无向图的方向性检验方法。对于弦图结构，我们证明了鞍点近似的精确性，由于仅涉及两个标量积分数值计算带来的近似误差，该检验能精确控制检验水平。虽然非弦图无法保证精确性，但鞍点近似在控制相对误差方面的优势，使方向性检验即便在此类场景下仍优于现有方法。通过具有挑战性的仿真实验验证了本方法的准确性——在似然比检验及其高阶修正的经典渐近近似均失效的情形下，本方法仍保持稳健。我们将该方向性方法应用于某兽医学牛群实验数据集，用以评估马尔可夫依赖性。另一组微阵列数据分析则展示了如何通过该方法选择与急性淋巴细胞白血病相关的基因异常图结构。