Statistics

Suppose that a data analyst wishes to report the results of a least squares linear regression only if the overall null hypothesis, $H_0^{1:p}: \beta_1= \beta_2 = \ldots = \beta_p=0$, is rejected. This practice, which we refer to as…

The sliced Wasserstein flow (SWF), a nonparametric and implicit generative gradient flow, is transformed into a Liouville partial differential equation (PDE)-based formalism. First, the stochastic diffusive term from the Fokker-Planck…

Unmeasured confounding, unethical exposure, and ill-defined interventions pose significant challenges to evaluating policy-relevant mediation estimands in medicine and public health. In observational studies involving harmful exposures, the…

Deep Gaussian Processes (DGPs) compose GP layers to warp inputs, enabling improved emulation of computer models with nonstationary input-output behavior compared with ordinary GPs. In contrast to GPs, the predictive uncertainty for DGP…

Epidemic models are invaluable tools to understand and implement strategies to control the spread of infectious diseases, as well as to inform public health policies and resource allocation. However, current modeling approaches have…

This paper addresses a fundamental but largely unexplored challenge in sequential changepoint analysis: conducting inference following a detected change. We develop a very general framework to construct confidence sets for the unknown…

Hyperparameter tuning is a key component of machine learning procedures, but when validation data contain sensitive user information, search mechanisms can leak private information through the selected configuration. Existing differentially…

Differences-in-differences (DiD) is a causal inference method for observational longitudinal data that assumes parallel expected potential outcome trajectories between treatment groups under the counterfactual scenario where all units…

Clinical assessments for neuromuscular disorders, such as Spinal Muscular Atrophy (SMA) and Duchenne Muscular Dystrophy (DMD), continue to rely on subjective measures to monitor treatment response and disease progression. We introduce a…

The Global Carbon Budget, maintained by the Global Carbon Project, summarizes Earth's global carbon cycle through four annual time series beginning in 1959: atmospheric CO$_2$ concentrations, anthropogenic CO$_2$ emissions, and CO$_2$…

Symmetry is ubiquitous in many real-world phenomena and tasks, such as physics, images, and molecular simulations. Empirical studies have demonstrated that incorporating symmetries into generative models can provide better generalization…

Discriminant analysis (DA) is one of the most popular methods for classification due to its conceptual simplicity, low computational cost, and often solid performance. In its standard form, DA uses the arithmetic mean and sample covariance…

Autism Spectrum Disorder (ASD) is a neurodevelopmental condition associated with difficulties with social interactions, communication, and restricted or repetitive behaviors. To characterize ASD, investigators often use functional…

R. A. Fisher introduced the fiducial distribution as a potential replacement for the Bayesian posterior distribution in the 1930s. During the past century, fiducial approaches have been explored in various parametric and nonparametric…

Understanding causal mechanisms is crucial for explaining and generalizing empirical phenomena. Causal mediation analysis offers statistical techniques to quantify the mediation effects. Although numerous methods have been developed for…

In this paper, we propose a novel high-dimensional time-varying coefficient estimator for noisy high-frequency observations with a factor structure. In high-frequency finance, we often observe that noises dominate the signal of underlying…

Digital technologies (e.g., mobile phones) can be used to obtain objective, frequent, and real-world digital phenotypes from individuals. However, modeling these data poses substantial challenges since observational data are subject to…

Existing rigorous convergence guarantees for the Hamiltonian Monte Carlo (HMC) algorithm use Gaussian auxiliary momentum variables, which are crucially symmetrically distributed. We present a novel convergence analysis for HMC utilizing new…

In many scientific areas, data with quantitative and qualitative (QQ) responses are commonly encountered with a large number of predictors. By exploring the association between QQ responses, existing approaches often consider a joint model…

With the recent paradigm shift from cytotoxic drugs to new generation of target therapy and immuno-oncology therapy during oncology drug developments, patients with various cancer (sub)types may be eligible to participate in a basket trial…