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With the increasing availability of datasets, developing data fusion methods to leverage the strengths of different datasets to draw causal effects is of great practical importance to many scientific fields. In this paper, we consider…

Methodology · Statistics 2023-07-18 Yijiao Zhang , Zhongyi Zhu

Inverse problems aim to determine model parameters of a mathematical problem from given observational data. Neural networks can provide an efficient tool to solve these problems. In the context of Bayesian inverse problems, Uncertainty…

Numerical Analysis · Mathematics 2025-09-16 Andrea Tonini , Tan Bui-Thanh , Francesco Regazzoni , Luca Dede' , Alfio Quarteroni

In this work, we propose an approach for assessing sensitivity to unobserved confounding in studies with multiple outcomes. We demonstrate how prior knowledge unique to the multi-outcome setting can be leveraged to strengthen causal…

Methodology · Statistics 2023-01-26 Jiajing Zheng , Jiaxi Wu , Alexander D'Amour , Alexander Franks

A key challenge in causal inference from observational studies is the identification and estimation of causal effects in the presence of unmeasured confounding. In this paper, we introduce a novel approach for causal inference that…

Methodology · Statistics 2022-10-17 Ying Zhou , Dingke Tang , Dehan Kong , Linbo Wang

We study the problem of learning conditional average treatment effects (CATE) from observational data with unobserved confounders. The CATE function maps baseline covariates to individual causal effect predictions and is key for…

Machine Learning · Statistics 2018-10-09 Nathan Kallus , Xiaojie Mao , Angela Zhou

Quantile regression (QR) is a statistical tool for distribution-free estimation of conditional quantiles of a target variable given explanatory features. QR is limited by the assumption that the target distribution is univariate and defined…

Counterfactual distributions are important ingredients for policy analysis and decomposition analysis in empirical economics. In this article we develop modeling and inference tools for counterfactual distributions based on regression…

Methodology · Statistics 2017-11-23 Victor Chernozhukov , Ivan Fernandez-Val , Blaise Melly

We develop a predictive inference procedure that combines conformal prediction (CP) with unconditional quantile regression (QR) -- a commonly used tool in econometrics that involves regressing the recentered influence function (RIF) of the…

Machine Learning · Computer Science 2023-04-05 Ahmed M. Alaa , Zeshan Hussain , David Sontag

This paper provides a method to construct simultaneous confidence bands for quantile functions and quantile effects in nonlinear network and panel models with unobserved two-way effects, strictly exogenous covariates, and possibly discrete…

Econometrics · Economics 2020-06-09 Victor Chernozhukov , Iván Fernández-Val , Martin Weidner

Treatment effects in a wide range of economic, environmental, and epidemiological applications often vary across space, and understanding the heterogeneity of causal effects across space and outcome quantiles is a critical challenge in…

Methodology · Statistics 2025-09-03 Yan Gong , Reetam Majumder , Brian J. Reich , Raphaël Huser

U-statistics constitute a large class of estimators, generalizing the empirical mean of a random variable $X$ to sums over every $k$-tuple of distinct observations of $X$. They may be used to estimate a regular functional $\theta(P_{X})$ of…

Statistics Theory · Mathematics 2019-03-27 Alexis Derumigny

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) model - are strongly connected. In the form of conditional expectation the Bayesian update…

Numerical Analysis · Mathematics 2014-04-09 Alexander Litvinenko , Hermann G. Matthies

Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We…

Methodology · Statistics 2023-11-13 Minna Genbäck , Xavier de Luna

In this paper, we introduce the weighted-average quantile regression framework, $\int_0^1 q_{Y|X}(u)\psi(u)du = X'\beta$, where $Y$ is a dependent variable, $X$ is a vector of covariates, $q_{Y|X}$ is the quantile function of the…

Econometrics · Economics 2022-03-08 Denis Chetverikov , Yukun Liu , Aleh Tsyvinski

This study demonstrates the existence of a testable condition for the identification of the causal effect of a treatment on an outcome in observational data, which relies on two sets of variables: observed covariates to be controlled for…

Econometrics · Economics 2026-05-20 Martin Huber , Jannis Kueck

This paper deals with the problem of evaluating the causal effect using observational data in the presence of an unobserved exposure/ outcome variable, when cause-effect relationships between variables can be described as a directed acyclic…

Methodology · Statistics 2012-06-18 Manabu Kuroki , Zhihong Cai

Analyses of environmental phenomena often are concerned with understanding unlikely events such as floods, heatwaves, droughts or high concentrations of pollutants. Yet the majority of the causal inference literature has focused on…

Methodology · Statistics 2021-09-09 Shuo Sun , Erica E. M. Moodie , Johanna G. Nešlehová

This paper examines the problem of nonparametric testing for the no-effect of a random covariate (or predictor) on a functional response. This means testing whether the conditional expectation of the response given the covariate is almost…

Statistics Theory · Mathematics 2014-11-25 Valentin Patilea , Cesar Sanchez-Sellero , Matthieu Saumard

Although complete randomization is widely regarded as the gold standard for causal inference, covariate imbalance can still arise by chance in finite samples. Rerandomization has emerged as an effective tool to improve covariate balance…

Methodology · Statistics 2026-01-21 Tingxuan Han , Yuhao Wang

We propose a framework for determining whether the causal dependence of an outcome $Y$ on a covariate $X$ changes at a given time point, given confounders $\boldsymbol{Z}$. For instance, in financial markets, the effect of a market…

Methodology · Statistics 2026-05-08 Shakeel Gavioli-Akilagun , Kieran Wood , Francesco Quinzan