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:用于比较不完整非方向图形的定向测试是在高西亚图形模型共变选择的大背景下制定的。根基马鞍点近近似的准确性在chordal图形中得到了证明,并导致精确控制测试的大小,因为所涉及的唯一近似误差是由于对两个斜弧整体的数值计算造成的。虽然对非正弦图形来说,没有保证精确性,但马鞍点近似控制相对错误的能力导致方向测试超越其竞争者,即使在这些情况下也是如此。我们提案的准确性通过具有挑战性的设想下的模拟实验得到验证,在这种假设中,通过标准的准点近似误差对概率比测试及其某些较高顺序修改失败了推断。方向方法用来说明对牛畜兽医试验数据集中马科维尼依赖性的评估。第二个有微粒数据的例子表明如何选择与急性淋巴细胞性白血病引起的遗传异常有关的图表结构。