Related papers: A Potential Outcomes Calculus for Identifying Cond…
Obtaining a non-parametric expression for an interventional distribution is one of the most fundamental tasks in causal inference. Such an expression can be obtained for an identifiable causal effect by an algorithm or by manual application…
We present a symbolic machinery that admits both probabilistic and causal information about a given domain and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of…
The concept of causality has a controversial history. The question of whether it is possible to represent and address causal problems with probability theory, or if fundamentally new mathematics such as the do calculus is required has been…
Predicting potential and counterfactual outcomes from observational data is central to individualized decision-making, particularly in clinical settings where treatment choices must be tailored to each patient rather than guided solely by…
The do-calculus is a sound and complete tool for identifying causal effects in acyclic directed mixed graphs (ADMGs) induced by structural causal models (SCMs). However, in many real-world applications, especially in high-dimensional…
Given a causal graph, the do-calculus can express treatment effects as functionals of the observational joint distribution that can be estimated empirically. Sometimes the do-calculus identifies multiple valid formulae, prompting us to…
Causal inference is best understood using potential outcomes. This use is particularly important in more complex settings, that is, observational studies or randomized experiments with complications such as noncompliance. The topic of this…
This paper introduces Attribution Projection Calculus (AP-Calculus), a novel mathematical framework for determining causal relationships in structured Bayesian networks. We investigate a specific network architecture with source nodes…
The generalizability of empirical findings to new environments, settings or populations, often called "external validity," is essential in most scientific explorations. This paper treats a particular problem of generalizability, called…
Typical causal effects are defined based on the marginal distribution of potential outcomes. However, many real-world applications require causal estimands involving the joint distribution of potential outcomes to enable more nuanced…
Estimating causal queries, such as changes in protein abundance in response to a perturbation, is a fundamental task in the analysis of biomolecular pathways. The estimation requires experimental measurements on the pathway components.…
When causal quantities cannot be point identified, researchers often pursue partial identification to quantify the range of possible values. However, the peculiarities of applied research conditions can make this analytically intractable.…
When making treatment selection decisions, it is essential to include a causal effect estimation analysis to compare potential outcomes under different treatments or controls, assisting in optimal selection. However, merely estimating…
Estimation of individual treatment effects is commonly used as the basis for contextual decision making in fields such as healthcare, education, and economics. However, it is often sufficient for the decision maker to have estimates of…
A notion of probabilistic lambda-calculus usually comes with a prescribed reduction strategy, typically call-by-name or call-by-value, as the calculus is non-confluent and these strategies yield different results. This is a break with one…
Probabilities of Causation (PoC) play a fundamental role in decision-making in law, health care and public policy. Nevertheless, their point identification is challenging, requiring strong assumptions, in the absence of which only bounds…
Mechanisms for the automation of uncertainty are required for expert systems. Sometimes these mechanisms need to obey the properties of probabilistic reasoning. A purely numeric mechanism, like those proposed so far, cannot provide a…
This tutorial provides a concise introduction to modern causal modeling by integrating potential outcomes and graphical methods. We motivate causal questions such as counterfactual reasoning under interventions and define binary treatments…
Among Judea Pearl's many contributions to Causality and Statistics, the graphical d-separation} criterion, the do-calculus and the mediation formula stand out. In this chapter we show that d-separation} provides direct insight into an…
Mediation analysis seeks to infer how much of the effect of an exposure on an outcome can be attributed to specific pathways via intermediate variables or mediators. This requires identification of so-called path-specific effects. These…