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Semi-Berry Approximation for Scale-Homogeneous Sums of Random Variables: Lyapunov-Guided Partitioning Between Gaussian Aggregation and Targeted Simulation

This paper proposes a Semi-Berry approximation that partitions scale-homogeneous random variables into Gaussian-aggregated and simulation-targeted groups based on the Lyapunov ratio, significantly reducing tail quantile errors and computational costs compared to standard Normal approximations or full Monte Carlo simulations.

bing xiong2026-09-21
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A Mathematical Framework for Topological Causal Data Analysis

This paper introduces Topological Causal Data Analysis (TCDA), a framework that integrates stable topological summaries with causal inference to analyze structured outcomes like images and networks, providing identification, estimation, and consistency results for both individual and distribution-level causal effects while clarifying the limits of topology in causal discovery.

Hugo Gobato Souto, Ioannis Diamantis2026-09-18
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Communication-efficient distributed hazard difference estimation for heterogeneous multi-site survival data

The paper introduces DiSAH, a communication-efficient, non-iterative federated algorithm that enables multi-site estimation of hazard differences for survival analysis without sharing patient-level data, achieving accuracy comparable to centralized models while outperforming traditional meta-analysis and local approaches.

Ziwen Wang, Siqi Li, Marcus Eng Hock Ong, Nan Liu2026-09-18
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Rule-Aware Bayesian Reconstruction and Local Auditing of Hidden Crowd Preferences

This paper proposes a rule-aware Bayesian framework that reconstructs hidden crowd preferences in hybrid expert-crowd systems by modeling latent utilities through dynamic inverse-preference problems, enabling the auditing of aggregation trade-offs and the evaluation of counterfactual decision protocols across 33 seasons of televised competition data.

Yaorong Huang, Zhanhao Cai, Zhuohang Zhang, Yuntao Jia2026-09-18
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Incremental Predictive Value of Item-Adjusted Process Indicators for Mathematics Achievement among Korean Students in PISA 2022: A School-Level Out-of-Sample Validation Study

This study demonstrates that item-adjusted process indicators derived from computer-based assessments significantly improve the prediction of mathematics achievement among Korean students in PISA 2022 beyond traditional questionnaire data, even under a rigorous school-level out-of-sample validation design.

Hejing Li¹2026-09-18
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Fast Emulation, Modular Calibration, and Active Learning for Simulators with Functional Response

This paper introduces a highly scalable, modular emulator for functional-output simulators that leverages global Gaussian process lengthscale estimates to enable fast local regression, thereby facilitating efficient active learning and rapid calibration of complex multiphysics models while significantly reducing computational costs compared to fully Bayesian approaches.

Grant Hutchings, Derek Bingham, Kellin Rumsey, Earl Lawrence2026-09-17