统计学

Traditional step-stress accelerated life testing models assume that test units originate from a homogeneous population. Recently, Lu and Kateri (2025) proposed a heterogeneous cumulative exposure based SSALT model to account for the…

Net benefit is widely used and reported to evaluate the clinical utility of prediction models, yet its interpretation often remains difficult in practice. In this didactical note, we develop two complementary interpretations that make net…

While diffusion models have emerged as a powerful class of generative models, their learning dynamics remain poorly understood. We address this issue first by empirically showing that standard diffusion models trained on natural images…

Many statistical problems can be addressed by applying a multiple testing procedure (MTP) that controls either the Family-wise Error Rate (FWER) or False Discovery Rate (FDR) under unknown arbitrarily-interdependent $p$-values, without…

Understanding interaction effects among variables is important for regression modeling in various applications. The conventional approach of quantifying interactions as the product of variables often lacks clear interpretability, especially…

OBJECTIVE: To propose time-to-event estimators that help evaluate incident diagnostic coding and possible upcoding in Medicare as well as introduce an open-source software package that enables more reproducible methods development relevant…

We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…

In developing data-driven modeling methodologies, there is an ongoing need to reconcile the strong predictive performance of opaque black-box models with the transparency required for critical applications. This work introduces an…

Two-phase sampling offers a cost-effective way to validate error-prone covariate measurements in biomedical databases. Inexpensive or easy-to-obtain information is collected for the entire study in Phase I. Then, a subset of patients…

Determining whether vaccine efficacy wanes is important for individual and public decision making. Yet, quantification of waning is a subtle task. The classical approaches cannot be interpreted as measures of declining efficacy unless we…

Variational inference (VI) is a cornerstone of modern Bayesian learning, enabling approximate inference in complex models. However, its formulation depends on expectations and divergences defined through high-dimensional integrals, often…

This paper investigates a recursive formulation of auto-regressive multi-fidelity Gaussian process regression in the challenging setting of noisy and non-nested high- and low-fidelity data. We propose a decoupled optimization strategy based…

Detecting multimodality in empirical distributions is a fundamental problem in statistics and data analysis, with applications ranging from clustering to the study of complex systems. In practice, however, assessing departures from…

The analysis of platform trials can be enhanced by utilizing non-concurrent controls. Since including this data might also introduce bias in the treatment effect estimators if time trends are present, methods for incorporating…

The solar spectral irradiance (SSI) depicts the spectral distribution of solar energy flux reaching the top of the Earth's atmosphere. Daily SSI measurements constitute a matrix with spectrally (rows) and temporally (columns) resolved solar…

Variational inference, as an alternative to Markov chain Monte Carlo sampling, has played a transformative role in enabling scalable computation for complex Bayesian models. Nevertheless, existing approaches often depend on either rigid…

This Element offers a practical guide to estimating conditional marginal effects-how treatment effects vary with a moderating variable-using modern statistical methods. Commonly used approaches, such as linear interaction models, often…

The multi-armed bandits (MAB) framework is a widely used approach for sequential decision-making, where a decision-maker selects an arm in each round with the goal of maximizing long-term rewards. In many practical applications, such as…

Large language models (LLMs) are increasingly used to simulate survey responses, but synthetic data can be misaligned with the human population, leading to unreliable inference. We develop a general framework that converts LLM-simulated…

Traditionally, studies in experimental physiology have been conducted in small groups of human participants, animal models or cell lines. Identifying optimal study designs that achieve sufficient power for drawing proper statistical…