统计学

The Sliced Wasserstein (SW) distance has emerged as a computationally attractive alternative to the Wasserstein distance by leveraging one-dimensional optimal transport along random projections. Standard estimators of the SW distance rely…

These notes recapitulate the high level mathematical principles behind different techniques for generative modeling. I show the connections between optimal transport and standard techniques such as Schr{\"o}dinger bridge and flow matching.

We propose an extension of the ordered stereotype model (OSM) for ordinal time series data, referred to as the Autoregressive OSM (AR-OSM). The model captures serial dependence by incorporating lagged values of the response as covariates in…

This study proposes coarse-to-fine downscaling (CF-DS), a scalable spatial downscaling method extending coarse-to-fine spatial modeling. Unlike conventional spatial-statistical downscaling methods such as area-to-point kriging, CF-DS does…

Reliable generative AI models critically rely on expert human annotations to evaluate output quality, yet these "gold" labels are expensive to collect and limited in quantity. Organizations thus often turn to collecting vast but noisy…

Large language models (LLMs) are interactive stochastic systems whose most consequential behaviors are still only partially understood. This discussion argues that statistics curricula should treat LLMs not only as tools, but as objects of…

Classical hypothesis testing frameworks break down in contemporary settings in which null hypotheses are increasingly abstract, the same data are used to both generate and test hypotheses, and minimal assumptions about the underlying data…

This paper examines how metric adjustments to Multidimensional Scaling (MDS) can enhance its effectiveness as a visual tool for pattern recognition. The distance under consideration, referred to as Max-D-SW, is an adjustment of the…

Transfer learning leverages knowledge from related source domains to improve learning in a target domain. Recent theoretical advances cover a broad range of regression settings within (generalized) linear models. Despite their diversity,…

Latent class models are central tools for multivariate categorical data from heterogeneous populations, but their standard local-independence assumption is often unrealistic in modern high-dimensional applications. We propose a…

This work presents a new bidirectional autoregressive latent diffusion approach for predicting the evolution of multiple fields (mass density, pressure, velocity, and magnetic field components) for magnetohydrodynamics. We show that this…

In this paper, we propose a model-based framework to robustify inference for circular data in the presence of anomalous observations, distinguishing between mild and gross anomalies. Starting from a unimodal and symmetric reference model on…

Accurate and scalable land cover classification is essential for global conservation monitoring and policy-making. While remote sensing images provide a cost-effective alternative to ground surveys, current methods often lack principled…

Conformal prediction guarantees marginal coverage, but pooled calibration averages over heterogeneous regions and can mask regional undercoverage in safety-critical subgroups. We introduce Self-Organized Conformal Prediction (SOCP), a…

Inferring the direction of a gene-regulatory relationship is harder than inferring whether a relationship exists, and most direction-inference methods are validated mainly on a single in silico benchmark. We ask which method remains…

The paper "Use of roster charts in the investigation and prosecution of nurses suspected of inflicting deliberate harm on patients" by Prof. John O'Quigley explores an interesting hypothesis concerning statistical information hidden in the…

Classical actuarial pricing models, such as the generalized linear model, are valued for transparency and ease of governance, but they use interactions among risk factors only when these are supplied through explicit feature engineering. We…

Gradient boosting in the form of decision tree ensembles has successfully been applied to a variety of problems using simple objective functions based on log-likelihoods of a single variable. The concept extends naturally to objective…

In recent years, models based on the Transformer architecture have seen widespread applications and have become one of the core tools in the field of deep learning. Numerous successful techniques, such as parameter-efficient fine-tuning and…

Bayesian statistics makes inference based on Bayes' theorem, but the posterior distribution of unknown parameters is typically analytically intractable. To estimate the posterior, two widely used numerical approximation methods are Markov…