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类别型工具变量模型：刻画、部分识别与统计推断AI 解读

We study categorical instrumental variable (IV) models with instrument, treatment and outcome taking finitely many values. We derive a simple closed-form characterization of the set of joint distributions of potential outcomes that are compatible with a given observed data distribution in terms of a minimal set of inequalities. These inequalities unify several different IV models defined by versions of the independence and exclusion restriction assumptions. They lead to…

示证型实验AI 解读

Adaptive experiments are used extensively in online platforms, healthcare and biotechnology, and the social sciences. Often, the primary goal is not to precisely estimate a treatment effect but to demonstrate that at least one candidate intervention yields a positive effect, for some subpopulation and on some measured outcome. We formalize this objective as testing the global null in a threshold bandit framework, and develop two inference procedures that are valid under…

个体处理效应的预测区间与锐界AI 解读

Individual treatment effect (ITE) is often regarded as the ideal target of inference in causal analyses and has been the focus of several recent studies. In this paper, we describe the intrinsic limits regarding what can be learned concerning ITEs given data from large randomized experiments. We consider when a valid prediction interval for the ITE is informative and when it can be bounded away from zero. The joint distribution over potential outcomes is only partially…

两个随机变量之和的分布界：重访Kolmogorov问题及个体处理效应应用AI 解读

We revisit the following problem, proposed by Kolmogorov: given prescribed marginal distributions $F$ and $G$ for random variables $X,Y$ respectively, characterize the set of compatible distribution functions for the sum $Z=X+Y$. Bounds on the distribution function for $Z$ were first given by Markarov (1982) and Rüschendorf (1982) independently. Frank et al. (1987) provided a solution to the same problem using copula theory. However, though these authors obtain the same…

工具变量模型中的假设与界限AI 解读

In this note we give proofs for results relating to the Instrumental Variable (IV) model with binary response $Y$ and binary treatment $X$, but with an instrument $Z$ with $K$ states. These results were originally stated in Richardson & Robins (2014), "ACE Bounds; SEMS with Equilibrium Conditions," arXiv:1410.0470.

统计因果性的潜在结果与决策理论基础AI 解读

In a recent paper published in the Journal of Causal Inference, Philip Dawid has described a graphical causal model based on decision diagrams. This article describes how single-world intervention graphs (SWIGs) relate to these diagrams. In this way, a correspondence is established between Dawid's approach and those based on potential outcomes such as Robins' Finest Fully Randomized Causally Interpreted Structured Tree Graphs. In more detail, a reformulation of Dawid's…