Statistics
The aim of survey statistics is to produce estimates with a minimal bias and a corresponding acceptable variance given a specific budget, preferable with a minor response burden for the participants. In recent years, considerable efforts…
The bootstrap is a foundational tool in statistical inference, but its classical implementation relies on Monte Carlo resampling, introducing approximation error and incurring high computational cost -- especially for large datasets and…
Canonical correlation analysis is a classic well-known multivariate statistical method focusing on the relationships between two sets of variables. The visualisation of those relationships can be achieved by means of a biplot of the…
Overlap, also known as positivity, is a key condition for causal treatment effect estimation. Many popular estimators suffer from high variance and become brittle when features differ strongly across treatment groups. This is especially…
The estimation of inequality and poverty measures is frequently constrained by a lack of individual data. Many countries, including China, continue to report income data in the form of aggregated income shares. In this context, the Beta…
Gaussian processes (GPs) offer appealing properties but are costly to train at scale. Sparse variational GP (SVGP) approximations reduce cost yet still rely on Cholesky decompositions of kernel matrices, ill-suited to low-precision,…
Stochastic natural gradient variational inference (NGVI) is a popular and efficient algorithm for Bayesian inference. Despite empirical success, the convergence of this method is still not fully understood. In this work, we define and study…
System outputs in Structural Health Monitoring (SHM), such as sensor measurements or extracted features like eigenfrequencies, are influenced not only by (potential) damage but also by environmental and operational variables (EOV).…
In the realm of high-dimensional data analysis, the estimation of covariance matrices is a fundamental task, and this holds true for interval-valued data as well. However, there is no unified definition for the covariance matrix of…
The scenario approach provides a powerful data-driven framework for designing solutions under uncertainty with rigorous probabilistic robustness guarantees. Existing theory, however, primarily addresses assessing robustness with respect to…
Modern medical research demands specialized causal inference methods evaluating complex continuous-time dynamic treatment regimens using observational data. For instance, obtaining the causal effects of intravenous administration, a…
Statistical inference on large-dimensional tensor data has been extensively studied in the literature and widely used in economics, biology, machine learning, and other fields, but how to generate a structured tensor with a target…
We study the problem of reconstructing the latent geometry of a $d$-dimensional Riemannian manifold from a random geometric graph. While recent works have made significant progress in manifold recovery from random geometric graphs, and more…
Linear stochastic transitivity is a central assumption in paired comparison models that is rarely verified in practice. Empirical violations, however, are common and can substantially affect inference and ranking. We develop a class of…
Meta-analyses are regarded as the highest level in the hierarchy of evidence, yet standard models traditionally concentrated on estimating the mean effect size, often under restrictive assumptions about the underlying distribution, such as…
One-shot federated learning enables multi-site inference with minimal communication. However, sharing summary statistics can still leak sensitive individual-level information when sites have only a small number of patients. In particular,…
Evaluating the causal effect of an intervention on multivariate outcomes is challenging when the outcomes are interdependent and derived rather than directly observed. Effective connectivity, which summarizes the directional neural…
Drug overdose mortality in the United States exhibits strong geographic heterogeneity and complex temporal evolution, yet most spatiotemporal studies focus on trends and risks without explicitly characterizing the underlying dynamical…
We propose a multivariate, distribution-free ranking framework for comparing clustered, correlated outcomes across groups, motivated by the evaluation of state-level policy environments using county-level socioeconomic data. Using pooled…
Grokking occurs when a model achieves high training accuracy but generalization to unseen test points happens long after that. This phenomenon was initially observed on a class of algebraic problems, such as learning modular arithmetic…