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All scientific interpretations of statistical outputs depend on background (auxiliary) assumptions that are rarely delineated or explicitly interrogated. These include not only the usual modeling assumptions, but also deeper assumptions…

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…

We address the challenge of explaining counterfactual outcomes in multi-agent Markov decision processes. In particular, we aim to explain the total counterfactual effect of an agent's action on the outcome of a realized scenario through its…

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…

Measuring conditional dependence is an important topic in statistics with broad applications including graphical models. Under a factor model setting, a new conditional dependence measure based on projection is proposed. The corresponding…

Measuring conditional dependencies among the variables of a network is of great interest to many disciplines. This paper studies some shortcomings of the existing dependency measures in detecting direct causal influences or their lack of…

This paper discusses the fundamental principles of causal inference - the area of statistics that estimates the effect of specific occurrences, treatments, interventions, and exposures on a given outcome from experimental and observational…

In this paper we investigate the notion of conditional independence and prove several information inequalities for conditionally independent random variables.

Consider the case where causal relations among variables can be described as a Gaussian linear structural equation model. This paper deals with the problem of clarifying how the variance of a response variable would have changed if a…

As a crucial problem in statistics is to decide whether additional variables are needed in a regression model. We propose a new multivariate test to investigate the conditional mean independence of Y given X conditioning on some known…

Evaluation of counterfactual queries (e.g., "If A were true, would C have been true?") is important to fault diagnosis, planning, determination of liability, and policy analysis. We present a method of revaluating counterfactuals when the…

The capacity to address counterfactual "what if" inquiries is crucial for understanding and making use of causal influences. Traditional counterfactual inference, under Pearls' counterfactual framework, typically depends on having access to…

For counterfactual policy evaluation, it is important to ensure that treatment parameters are relevant to policies in question. This is especially challenging under unobserved heterogeneity, as is well featured in the definition of the…

Identification of standard mediated effects such as the natural indirect effect relies on heavy causal assumptions. By circumventing such assumptions, so-called randomized interventional indirect effects have gained popularity in the…

Conditional independence is a fundamental concept in many areas of statistical research, including, for example, sufficient dimension reduction, causal inference, and statistical graphical models. In many modern applications, data arise in…

Counterfactuals are central in causal human reasoning and the scientific discovery process. The uplift, also called conditional average treatment effect, measures the causal effect of some action, or treatment, on the outcome of an…

We develop a novel method for counterfactual analysis based on observational data using prediction intervals for units under different exposures. Unlike methods that target heterogeneous or conditional average treatment effects of an…

Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provides a unified framework for both random and non-stochastic variables. The original paper establishes…

In this paper, we develop a unified regression approach to model unconditional quantiles, M-quantiles and expectiles of multivariate dependent variables exploiting the multidimensional Huber's function. To assess the impact of changes in…

This paper studies the unconditional effects of a general policy intervention, which includes location-scale shifts and simultaneous shifts as special cases. The location-scale shift is intended to study a counterfactual policy aimed at…