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Over the past few decades, addressing "spatial confounding" has become a major topic in spatial statistics. However, the literature has provided conflicting definitions, and many proposed solutions are tied to specific analysis models and…

When drawing causal inference from observational data, there is always concern about unmeasured confounding. One way to tackle this is to conduct a sensitivity analysis. One widely-used sensitivity analysis framework hypothesizes the…

Causal inference in observational studies can be challenging when confounders are subject to missingness. Generally, the identification of causal effects is not guaranteed even under restrictive parametric model assumptions when confounders…

Unmeasured confounding bias threatens the validity of observational studies. While sensitivity analyses and study designs have been proposed to address this issue, they often overlook the growing availability of auxiliary data. Using…

By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…

Hazard serves as a pivotal estimand in both practical applications and methodological frameworks. However, its causal interpretation poses notable challenges, including inherent selection biases and ill-defined populations to be compared…

We consider basic conceptual questions concerning the relationship between statistical estimation and causal inference. Firstly, we show how to translate causal inference problems into an abstract statistical formalism without requiring any…

Counterfactual fairness requires that a person would have been classified in the same way by an AI or other algorithmic system if they had a different protected class, such as a different race or gender. This is an intuitive standard, as…

Inferential challenges that arise when data are censored have been extensively studied under the classical frameworks. In this paper, we provide an alternative generalized inferential model approach whose output is a data-dependent…

Recent developments in the formalisation of quantum causal structures have made it possible to test and compare hypotheses about causal structure empirically, rather than being a-priori assumptions. Such differences in causal structure may…

For sensitivity analysis against unmeasured confounding, we build on the marginal sensitivity model (MSM) and propose a new model, deMSM, by incorporating a second constraint on the shift of potential outcome distributions caused by…

Estimating average causal effect (ACE) is useful whenever we want to know the effect of an intervention on a given outcome. In the absence of a randomized experiment, many methods such as stratification and inverse propensity weighting have…

It is generally believed that classical regime emerges as a limiting case of quantum theory. Exploring such quantum-classical correspondences in a more transparent manner is central to the deeper understanding of foundational aspects and…

Measurement error in the observed values of the variables can greatly change the output of various causal discovery methods. This problem has received much attention in multiple fields, but it is not clear to what extent the causal model…

Unmeasured confounding remains a critical challenge in causal inference for the social sciences. This paper proposes a sensitivity analysis framework to systematically evaluate how unmeasured confounders influence statistical inference in…

Many research questions concern treatment effects on outcomes that can recur several times in the same individual. For example, medical researchers are interested in treatment effects on hospitalizations in heart failure patients and sports…

Analysis of observational studies increasingly confronts the challenge of determining which of a possibly high-dimensional set of available covariates are required to satisfy the assumption of ignorable treatment assignment for estimation…

In epidemiological cohort studies, the relative risk (also known as risk ratio) is a major measure of association to summarize the results of two treatments or exposures. Generally, it measures the relative change in disease risk as a…

Causal inference studies whether the presence of a variable influences an observed outcome. As measured by quantities such as the "average treatment effect," this paradigm is employed across numerous biological fields, from vaccine and drug…

In this paper, we introduce and develop the concept of conditional quantization for Borel probability measures on $\mathbb{R}^k,$ considering both constrained and unconstrained frameworks. For each setting, we define the associated…