Statistics

Understanding vaccine effects on post-infection outcomes is critical for evaluating the full value proposition of a vaccine. However, defining appropriate causal effects on such outcomes is challenging because infection is affected by…

We study trajectory forecasting under squared loss for time series with weak conditional structure, using highly expressive prediction models. Building on the classical characterization of squared-loss risk minimization, we emphasize…

The low-rank matrix recovery problem seeks to reconstruct an unknown $n_1 \times n_2$ rank-$r$ matrix from $m$ linear measurements, where $m\ll n_1n_2$. This problem has been extensively studied over the past few decades, leading to a…

In Part I of this series, we established a rigorous mathematical isomorphism between ant colony decision-making and random forest learning, demonstrating that variance reduction through decorrelation is a universal principle shared by…

We propose closed-form conditional diffusion models for data assimilation. Diffusion models use data to learn the score function (defined as the gradient of the log-probability density of a data distribution), allowing them to generate new…

Delayed primary outcomes and administratively censored follow-up create a general semiparametric estimation problem: the target causal functional depends on an endpoint observed only for a shrinking subset of units at analysis time, while…

Hazard functions play a central role in survival analysis, providing insight into the underlying risk dynamics of time-to-event data, with broad applications in medicine, epidemiology, and related fields. First-order ordinary differential…

Learning the dependence structure among variables in complex systems is a central problem across medical, natural, and social sciences. These structures can be naturally represented by graphs, and the task of inferring such graphs from data…

The Mann-Whitney effect is an effect measure for the order of two sample-specific outcome variables. It has the interpretation of a probability and also a connection to the area under the ROC curve. In the literature it has been considered…

Intermittent demand forecasting poses unique challenges due to sparse observations, cold-start items, and obsolescence. Classical models such as Croston, SBA, and the Teunter--Syntetos--Babai (TSB) method provide simple heuristics but lack…

While generative models, especially large language models (LLMs), are ubiquitous in today's world, principled mechanisms to assess their (in)correctness are limited. Using the conformal prediction framework, previous works construct sets of…

We study the convergence of off-policy TD(0) with linear function approximation when used to approximate the expected discounted reward in a Markov chain. It is well known that the combination of off-policy learning and function…

Sequential analysis encompasses simulation theories and methods where the sample size is determined dynamically based on accumulating data. Since the conceptual inception, numerous sequential stopping rules have been introduced, and many…

Variational autoencoders (VAEs) are among leading approaches to address the problem of learning disentangled representations. Typically a single VAE is used and disentangled representations are sought within its single continuous latent…

We propose a generative multivariate posterior sampler via flow matching. It offers a simple training objective, and does not require access to likelihood evaluation. The method learns a dynamic, block-triangular velocity field in the joint…

Synthetic data can improve generalization when real data is scarce, but excessive reliance may introduce distributional mismatches that degrade performance. In this paper, we present a learning-theoretic framework to quantify the trade-off…

Structural equation modeling (SEM) is a prevalent approach for studying constructs.Traditionally, these constructs are modeled as reflectively measured latent variables - common factors that account for the variance-covariance structure of…

Introduction In analysis of time-to-event outcomes, a mixture cure (MC) model is preferred over a standard survival model when the sample includes individuals who will never experience the event of interest. Motivated by a cohort study of…

In this paper, we demonstrate a purely Bayesian approach for estimating within-group and between-group effect sizes for learning outcomes encountered in educational research, taking naturally into account the multilevel structure of the…

Flow cytometry is a valuable technique that measures the optical properties of particles at a single-cell resolution. When deployed in the ocean, flow cytometry allows oceanographers to study different types of photosynthetic microbes…