Statistics

We consider the problem of evaluating black-box multi-class classifiers. In the standard setup, we observe class labels $Y\in \{0,1,\ldots,M-1\}$ generated according to the conditional distribution $ Y|X \sim \text{…

We study language models as evolving model organisms and ask when autoregressive next-token learning selects for world-tracking representations. For any encoding of latent world states, the Bayes-optimal next-token cross-entropy decomposes…

Multimodal representation learning is commonly built on a shared-private decomposition, treating latent information as either common to all modalities or specific to one. This binary view is often inadequate: many factors are shared by only…

Large language model (LLM) evaluation platforms increasingly rely on pairwise human judgments. These data are noisy, sparse, and non-uniform, yet leaderboards are reported with limited uncertainty quantification. We study this as…

The classical Gaussian mixture model assumes homogeneity within clusters, an assumption that often fails in real-world data where observations naturally exhibit varying scales or intensities. To address this, we introduce the…

Ordinary differential equations (ODEs) provide a powerful framework for modeling dynamic systems arising in a wide range of scientific domains. However, most existing ODE methods focus on a single system, and do not adequately address the…

The sufficient cause framework has been used for decades to improve our understanding of both basic and more complex causal concepts in epidemiology, such as mediation and interaction. Here, we make use of this framework to provide a…

A statistical analysis of precipitation at Rio Grande do Sul State was presented in this article. The aim of this work was to identify spatial and temporal patterns of maximum precipitation, which was achieved by fitting a theoretical…

We study hypothesis testing for penalized estimators in settings where the full marginal distribution of a multivariate response is difficult to specify, such as longitudinal data with correlated measurements or high-dimensional…

This paper introduces a novel generative framework for synthesising forward-looking, c\`adl\`ag stochastic trajectories that are sequentially consistent with time-evolving path-law proxies, thereby incorporating anticipated structural…

We introduce the Hiremath Early Detection (HED) Score, a principled, measure-theoretic evaluation criterion for quantifying the time-value of information in systems operating over non-stationary stochastic processes subject to abrupt regime…

We develop a semi-parametric state-space model for time-series data with latent regime transitions. Classical Markov-switching models use fixed parametric transition functions, such as logistic or probit links, which restrict flexibility…

We study identification and inference in nonlinear dynamic systems defined on unknown interaction networks. The system evolves through an unobserved dependence matrix governing cross-sectional shock propagation via a nonlinear operator. We…

We propose a generalized win fraction regression framework for prioritized composite survival outcomes. The framework models the conditional win fraction through a chosen link function (including identity, logit, or probit), thereby…

Randomized controlled trials often do not represent the populations where decisions are made, and covariate shift across studies can invalidate standard IPD meta-analysis and transport estimators. We propose a placebo-anchored transport…

Instrumental variable (IV) methods mitigate bias from unobserved confounding in observational causal inference but rely on the availability of a valid instrument, which can often be difficult or infeasible to identify in practice. In this…

The ensemble Kalman filter (EnKF) is a popular technique for performing inference in state-space models (SSMs), particularly when the dynamic process is high-dimensional. Unlike reweighting methods such as sequential Monte Carlo (SMC, i.e.…

Covariate adjustment can enhance precision and power in clinical trials, yet its application to the win odds remains unclear. The win odds is an extension of the win ratio that counts ties as half a win for the treatment and the control…

Parametric partial differential equations (PDEs) serve as fundamental mathematical tools for modeling complex physical phenomena, yet repeated high-fidelity numerical simulations across parameter spaces remain computationally prohibitive.…

We propose an automatic approach for manifold nonlinear autoregressive with exogenous inputs (mNARX) modeling that leverages the feature-based structure of functional-NARX (F-NARX) modeling. This novel approach, termed mNARX+, preserves the…