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We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…

Causal inference is a statistical paradigm for quantifying causal effects using observational data. It is a complex process, requiring multiple steps, iterations, and collaborations with domain experts. Analysts often rely on visualizations…

Causal inference on multiple non-independent outcomes raises serious challenges, because multivariate techniques that properly account for the outcome's dependence structure need to be considered. We focus on the case of binary outcomes…

Causal discovery, the problem of inferring the direction of causality, is generally ill-posed. We use the language of structural causal models (SCM) to show that assuming that the causal relations are acyclic and invariant across multiple…

Instrumental variable methods are widely used for inferring the causal effect in the presence of unmeasured confounders. Existing instrumental variable methods for nonlinear outcome models require stringent identifiability conditions. This…

Two dimensional matrices with binary (0/1) entries are a common data structure in many research fields. Examples include ecology, economics, mathematics, physics, psychometrics and others. Because the columns and rows of these matrices…

In this article, we assess the benefits of coordination and partnerships between governments and private insurers, and provide further evidence for microinsurance products as powerful and cost-effective tools for achieving poverty…

Multiple imputation has become one of the standard methods in drawing inferences in many incomplete data applications. Applications of multiple imputation in relatively more complex settings, such as high-dimensional clustered data, require…

Electronic health records are a valuable data source for investigating health-related questions, and propensity score analysis has become an increasingly popular approach to address confounding bias in such investigations. However, because…

The assumption of independence between observations (units) in a dataset is prevalent across various methodologies for learning causal graphical models. However, this assumption often finds itself in conflict with real-world data, posing…

Causal inference is crucial for understanding the true impact of interventions, policies, or actions, enabling informed decision-making and providing insights into the underlying mechanisms that shape our world. In this paper, we establish…

This paper considers the problem of testing many moment inequalities where the number of moment inequalities, denoted by $p$, is possibly much larger than the sample size $n$. There is a variety of economic applications where solving this…

Evaluating the causal effect of an intervention on multivariate outcomes is challenging when the outcomes are interdependent and derived rather than directly observed. Effective connectivity, which summarizes the directional neural…

Income inequality is an important issue that has to be solved in order to make progress in our society. The study of income inequality is well received through the Gini coefficient, which is used to measure degrees of inequality in general.…

Decades of economic decline have led to areas of increased deprivation in a number of U.S. inner cities, which can be linked to adverse health and other outcomes. Yet the calculation of a single "deprivation" index, which has received wide…

We develop methodology for causal inference in observational studies when using propensity score subclassification on data constructed with probabilistic record linkage techniques. We focus on scenarios where covariates and binary treatment…

Cause-effect relationships are typically evaluated by comparing outcome responses to binary treatment values, representing two arms of a hypothetical randomized controlled trial. However, in certain applications, treatments of interest are…

A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their…

We study causal inference under case-control and case-population sampling. Specifically, we focus on the binary-outcome and binary-treatment case, where the parameters of interest are causal relative and attributable risks defined via the…

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors $W$ and $H$, for the given input matrix $A$, such that $A \approx W H$. NMF is a useful tool for many applications in different domains…