Related papers: Adding covariates to bounds: What is the question?

Causal inference is central to statistics and scientific discovery, enabling researchers to identify cause-and-effect relationships beyond associations. While traditionally studied within Euclidean spaces, contemporary applications…

We study the problem of estimating causal effects under hidden confounding in the following unpaired data setting: we observe some covariates $X$ and an outcome $Y$ under different experimental conditions (environments) but do not observe…

There is a large literature on semiparametric estimation of average treatment effects under unconfounded treatment assignment in settings with a fixed number of covariates. More recently attention has focused on settings with a large number…

The participants in randomized trials and other studies used for causal inference are often not representative of the populations seen by clinical decision-makers. To account for differences between populations, researchers may consider…

We present an overview of the decision-theoretic framework of statistical causality, which is well-suited for formulating and solving problems of determining the effects of applied causes. The approach is described in detail, and is related…

We develop a data-driven information-theoretic framework for sharp partial identification of causal effects under unmeasured confounding. Existing approaches often rely on restrictive assumptions, such as bounded or discrete outcomes;…

Using symmetric boundary conditions at separated times, I show analytically that both the time ordering of (macroscopic) causality and the direction of entropy increase follow from these boundary conditions. In particular, when the…

We assume to be given structural equations over discrete variables inducing a directed acyclic graph, namely, a structural causal model, together with data about its internal nodes. The question we want to answer is how we can compute…

We study the sharp bounds of $\mathbb{E}[X_1\cdots X_d]$ when the univariate marginal distributions are known, but the dependence structure between them is unspecified. Maximizing products over non-negative variables is straightforward via…

Mathematicians tend to use the phrase "arbitrarily close" to mean something along the lines of "every neighborhood of a point intersects a set". Taking the latter statement as a technical definition for arbitrarily close leads to an…

To answer questions of "causes of effects", the probability of necessity is introduced for assessing whether or not an observed outcome was caused by an earlier treatment. However, the statistical inference for probability of necessity is…

The goal of this paper is to design a causal inference method accounting for complex interactions between causal factors. The proposed method relies on a category theoretical reformulation of the definitions of dependent variables,…

Implicit variables of an optimization problem are used to model variationally challenging feasibility conditions in a tractable way while not entering the objective function. Hence, it is a standard approach to treat implicit variables as…

Statisticians usually restrict regression to model relationships that are explicitly defined dependent and independent random variables; this paper outlines the newly developed method of non-response analysis and rotational analysis for…

Causal inference plays an important role in explanatory analysis and decision making across various fields like statistics, marketing, health care, and education. Its main task is to estimate treatment effects and make intervention…

We study a generalization of conditional probability for arbitrary ordered vector spaces. A related problem is that of assigning a numerical value to one vector relative to another. We characterize the groups for which these generalized…

The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments,…

An apriori bound for the condition number associated to each of the following problems is given: general linear equation solving, minimum squares, non-symmetric eigenvalue problems, solving univariate polynomials, solving systems of…

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing…

Calibration weighting has been widely used to correct selection biases in non-probability sampling, missing data, and causal inference. The main idea is to calibrate the biased sample to the benchmark by adjusting the subject weights.…