Statistics Seminar Series

Uncovering Hidden Treatment Effect Heterogeneity Through Optimal Transport

The conditional average treatment effect has all but become synonymous with “treatment effect heterogeneity.” However, treatment impacts the entire outcome distribution, not just its mean. Thus, there are two sources of heterogeneity to consider: across covariate strata and across quantiles. We develop a framework for characterizing and testing for both types of heterogeneous effects using the Wasserstein geometry. Specifically, we treat the difference between conditional quantile functions as a surface indexed by covariates and quantiles. This allows us to distinguish between covariate heterogeneity, rank heterogeneity, and covariate-rank interactions. The average of this surface over ranks is the conditional average treatment effect, and its norm is the conditional Wasserstein distance. We then define integrated distributional effects that aggregate distributional movement across strata; this allows us to measure the amount of distributional heterogeneity hidden by marginal analyses. For each new estimand, we develop efficient influence functions, estimation procedures, and interpretable tests. Furthermore, we generalize our framework to multivariate outcomes by exploring integrated Sinkhorn effects. Finally, we validate our theoretical results via simulation and apply our methods to a real-world dataset. Our framework thus unifies mean and distributional notions of heterogeneity.

Spatial Statistical Modeling of Neuroimaging Data and Drug Addiction

High-resolution neuroimaging data provide unprecedented opportunities to study brain structure and function, but their massive dimensionality and complex spatial dependence create fundamental statistical challenges. Magnetic resonance imaging (MRI), for example, may contain millions of spatially correlated voxels. Fully modeling this dependence is computationally prohibitive, leading many approaches to aggregate information into predefined regions of interest (ROIs). Although convenient, such aggregation can obscure fine-scale spatial structure, diminish power to detect localized effects, and potentially alter scientific conclusions. We introduce a novel Bayesian tensor regression framework for modeling neuroimaging data directly at the voxel level, avoiding the need to collapse the brain into predefined regions. The brain image is represented as a tensor-valued response, allowing covariate effects and spatial dependence to be modeled across its natural multidimensional structure. A generalized sparsity formulation makes inference feasible at very high dimensions while preserving scientifically meaningful spatial information. The fully Bayesian framework also provides coherent quantification of uncertainty through computational algorithms designed for large-scale tensor data. We apply the methodology to neuroimaging studies of drug addiction, with particular emphasis on cocaine dependence and its effects on brain structure and function. Simulation studies and empirical analyses demonstrate improved identification of spatially localized patterns and a richer characterization of brain alterations associated with addiction. More broadly, this work shows how spatial statistics can move neuroimaging analysis beyond coarse regional summaries toward scalable, uncertainty-aware inference at the resolution at which brain changes are actually observed.

New Opportunities in Fake Data

Stochastic computer simulation—literally, the generation of “fake data”—is a practical tool for the design and improvement of dynamic systems that are subject to uncertainty. Research in and application of stochastic simulation sits at the interface of industrial engineering/operations research, computer science, and statistics. Ubiquitous parallel computing and the need for system control through digital twins have created new opportunities that require new ways of thinking about simulation. This talk introduces two of these opportunities through real applications. The presentation is math-light and begins with an audience-participation simulation that demonstrates the key ideas.

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