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秩变换子抽样：多次数据拆分与可交换 p 值的推断AI 解读

Abstract Many testing problems are readily amenable to randomized tests, such as those employing data splitting. However, despite their usefulness in principle, randomized tests have obvious drawbacks. Firstly, two analyses of the same dataset may lead to different results. Secondly, the test typically loses power because it does not fully utilize the entire sample. As a remedy to these drawbacks, we study how to combine the test statistics or p-values resulting from…

Richard Guo 对《因果模型的参数化与模拟》的讨论：两种分解与密度比AI 解读

I congratulate Evans and Didelez warmly on this innovative and inspiring paper. Here, I offer my interpretation of the approach in terms of two factorizations and a density ratio. Any distribution over Z,X,Y can be factorized in two ways: Factorization C−1 is the usual one; it is factorization A−1 that is the focus of the two authors. More concretely, suppose ϕZY∣X(z,y∣x) is a conditional copula density, i.e. for every value of x, (z,y)↦ϕZY∣X(z,y∣x) is a density function…

变量消除、图约简与有效 g 公式AI 解读

Summary We study efficient estimation of an interventional mean associated with a point exposure treatment under a causal graphical model represented by a directed acyclic graph without hidden variables. Under such a model, a subset of the variables may be uninformative, in that failure to measure them neither precludes identification of the interventional mean nor changes the semiparametric variance bound for regular estimators of it. We develop a set of graphical criteria…

边际独立与条件独立的检验AI 解读

Summary We consider testing marginal independence versus conditional independence in a trivariate Gaussian setting. The two models are nonnested, and their intersection is a union of two marginal independences. We consider two sequences of such models, one from each type of independence, that are closest to each other in the Kullback–Leibler sense as they approach the intersection. They become indistinguishable if the signal strength, as measured by the product of two…