Title: Robust trial augmentation using external data

Abstract: Randomized trials often have sample sizes that are too small to produce precise estimates of treatment effects. One approach for improving trial efficiency is to incorporate external data from previously completed trials or observational studies into the estimation process. When the external data are aligned with the trial data and statistical models for nuisance functions are correctly specified, using the external data can yield consistent estimates and enhance efficiency. 

Some degree of misalignment or misspecification, however, is usually expected and can threaten trial validity. We develop a class of estimators that exploit randomization to ensure consistency and asymptotic normality, even when the external data are misaligned with the trial. We also propose a procedure that uses members of this class to construct a combined estimator that is consistent and asymptotically normal and can leverage external data even when that data are misaligned with the trial, or when models for nuisance functions are mis-specified or have slow convergence rates. 

We show that the efficiency of the combined estimator is no lower than that of each of its component estimators (including the efficient trial-only estimator, if it is used as a component for the combined estimator). Our methods allow investigators to use external data to improve the trial's efficiency without concern for misalignment between the external data and the trial. We examine the finite-sample behavior of the proposed methods in simulation studies and apply them to analyze data from a trial comparing coronary artery bypass grafting surgery plus medical therapy versus medical therapy alone for patients with chronic coronary artery disease.

Title: Statistical ranking with dynamic covariates

Abstract: The Plackett–Luce (PL) model has long been used for rank aggregation in sports analytics and social choice. In this talk, we introduce a covariate-assisted ranking model within the PL framework that incorporates dynamic covariates. This added flexibility enables individualized and dynamic rankings and improves model fit, but it also introduces challenges for analysis. We address these challenges in the context of maximum likelihood estimation (MLE) under a general network topology. Specifically, we establish conditions for model identifiability and the unique existence of the MLE, propose an alternating maximization algorithm for computing the MLE, and prove a uniform consistency result. We illustrate the proposed model through applications to ATP tennis data spanning the past 40+ years and to a horse racing dataset.

Title: Designing Intelligent AI: Insights from Human Cognition

Abstract: Modern AI systems are evolving from passive tools toward agent-based systems that can reason, learn and interact with their environments. This talk discusses emerging research directions in generative AI, drawing inspiration from principles of human cognition including continuous learning and adaptation, effective knowledge transfer and multi-objective decision making. The goal is to stimulate new perspectives on building domain-aware and trustworthy AI systems that can operate reliably in complex, real-world settings.

Title: Bayesian Model Criticism: From Holdout Checks to Model Comparison

Abstract: In this talk, I will cover two recent works on Bayesian model criticism. The first is Holdout Predictive Checks (HPCs). HPCs are built on posterior predictive checks (PPCs), which check a model by assessing the posterior predictive distribution on the observed data. PPCs, however, use the data twice: to calculate the posterior predictive and to evaluate it.  This situation can lead to uncalibrated p-values. HPCs, in contrast, compare the posterior predictive distribution to a draw from the population distribution, a held-out dataset. This method blends Bayesian modeling with frequentist assessment. 

Unlike the PPC, we prove that the HPC is properly calibrated. Empirically, we study HPCs on classical regression, a hierarchical model of text data and factor analysis. In the second work, we introduce the posterior predictive null check (PPN), a method for Bayesian model criticism that helps characterize the relationships between models. The idea behind the PPN is to check whether data from one model's predictive distribution can pass a predictive check designed for another model. This form of criticism complements the classical predictive check by providing a comparative tool. 

A collection of PPNs, which we call a PPN study, can help us understand which models are equivalent and which models provide different perspectives on the data. With mixture models, we demonstrate how a PPN study, along with traditional predictive checks, can help select the number of components by the principle of parsimony. With probabilistic factor models, we demonstrate how a PPN study can help understand relationships between different classes of models, such as linear models and models based on neural networks. Finally, we also discuss ongoing work on aggregated posterior checks.

Title: Doubly robust estimation of causal effects for random object outcomes with continuous treatments 

Authors: Satarupa Bhattacharjee, Bing Li, Xiao Wu, Lingzhou Xue

Abstract: Causal inference is central to statistics and scientific discovery, enabling researchers to identify cause-and-effect relationships beyond associations. Although traditionally studied within Euclidean spaces, contemporary applications increasingly involve complex, non-Euclidean data structures that reside in abstract metric spaces known as random objects, such as images, shapes, networks, and distributions. 

This paper introduces a novel framework for causal inference with continuous treatments applied to non-Euclidean data. To address the challenges posed by the lack of linear structures, we leverage Hilbert space embeddings of the metric spaces to facilitate Frechet mean estimation and causal effect mapping. Motivated by a study on the impact of exposure to fine particulate matter on age-at-death distributions across U.S. counties, we propose a nonparametric, doubly-debiased causal inference approach for outcomes as random objects with continuous treatments. 

Our framework accommodates moderately high-dimensional vector-valued confounders and derives efficient influence functions for estimation, ensuring both robustness and interpretability. We establish asymptotic properties of the cross-fitted estimators and employ conformal inference techniques for counterfactual outcome prediction. Validated in both simulation and real-world environmental application, our framework extends causal inference methodologies to complex data structures, broadening its applicability across scientific disciplines.

Kickoff Event for the Department of History's CELEBRATING 1776 Series

This event will now be virtual. Click here to join

Join us for a lecture by Pulitzer Prize winner Joseph Ellis, moderated by University of Kentucky professor Amy Murrell Taylor.

About Joseph Ellis

The author of 12 books, Ellis was awarded the Pulitzer Prize for "Founding Brothers: The Revolutionary Generation" and won the National Book Award for "American Sphinx," a biography of Thomas Jefferson. He has taught at Mount Holyoke College, the University of Massachusetts and the U.S. Military Academy at West Point. His commentaries have been featured on CSPAN, CNN, and PBS’s News Hour, and he appears in the major new PBS documentary "The American Revolution."

Ellis’ latest work, "The Great Contradiction," examines how a government that had been justified and founded on the principles articulated in the Declaration of Independence institutionalized slavery and created a tidal wave of western migration by settlers who understood the phrase “pursuit of happiness” to mean the pursuit of Indian lands.

Click here to join virtually

Join us for Annual Graduate Alumni Day, where three UK Mathematics alumni from the University of South Florida, Georgia Tech, and Microsoft return to share the career paths and insights from life in and beyond academia. Come ready to listen, ask and leave with a clearer picture of what's possible.

Schedule:

• 2:00 PM — Mathematicians in the Age of Technology | Tefjol Pllaha, University of South Florida
• 3:00 PM — An Academic Professional Does What? | Hunter Lehmann, Georgia Institute of Technology
• 4:30 PM — Life After the Ph.D.: Research Beyond Academia | Vasily Zadorozhnyy, Microsoft

Dr. Sang Mo Yang, Sogang University, South Korea

Title: Ferroelectricity at the Nanoscale: Emerging Materials and Local Probes

Abstract: Ferroelectricity on the nanoscale has been the subject of considerable interest in condensed matter physics for over half a century. Beyond its fundamental importance, ferroelectricity provides essential functionality for advanced electronic devices, including nonvolatile memories, field-effect transistors and tunnel junctions. 

However, conventional perovskite-based ferroelectric oxides (e.g., Pb(Zr,Ti)O3) face significant challenges in achieving device performance that can compete with current dynamic random-access memories and flash memories. Over the past decade, novel ferroelectricity has been discovered in new material systems, including fluorite-structured HfO2-based thin films, two-dimensional (2D) van der Waals (vdW) materials and 2D perovskite halides. These discoveries have brought about a renaissance in the ferroelectric research community. 

In this colloquium, I will present our group’s recent efforts to investigate and understand ferroelectricity across these emerging material platforms [1] using various scanning probe microscopy techniques.
[1] T. H. Jung et al., “Spatially Resolved Observation of Ferroelectric-to-Paraelectric Phase Transition in a Two-Dimensional Halide Perovskite,” Advanced Materials 37, 2506270 (2025)