数据分析、统计与概率：2025–2026 年度综述

An annual survey of the physics.data-an arXiv category, covering research published from September 2025 – August 2026. Built on a close-reading set of 108 papers and organised into 40 chapters, it maps the year by the field's research sub-directions.

Book framework (share of the year's output):

• Non-Gaussian Distributions and Cross-Correlations in Complex Systems (16.3%) — This cluster focuses on characterizing non-Gaussian probability distributions, long-range correlations, and random matrix limits in complex systems such as financial markets, comets, and spin glasses.
• Imaging and Spectral Reconstruction with Machine Learning (15.6%) — This cluster addresses the use of machine learning and pattern recognition for phase identification, spectral reconstruction, and detector signal analysis in X-ray, gamma-ray, and imaging applications.
• Data-Driven Discovery and Surrogate Modeling in Physical Sciences (15.5%) — This cluster develops data-driven methods, including symbolic regression and surrogate models, to discover governing equations and accelerate design under uncertainty in physical systems.
• Machine Learning for Particle Physics and Detector Analysis (11.6%) — This cluster applies machine learning techniques to particle physics, including jet tagging, transfer learning, and point spread function modeling, to improve detector performance and physics inference.
• Temporal Networks and Higher-Order Interactions in Complex Systems (10.5%) — This cluster investigates temporal networks, higher-order interactions, and information-theoretic measures to model dependencies and reconstruction in systems ranging from optical networks to particle collisions.
• Gravitational Wave Detection and Anomaly Search in Physics Data (10.0%) — This cluster focuses on developing statistical and machine learning methods for gravitational wave detection, anomaly detection, and signal searches in large physics datasets.
• Bayesian Inference and Uncertainty Quantification in Physics (7.5%) — This cluster develops Bayesian hierarchical models, uncertainty quantification, and parameter estimation techniques for physics applications ranging from nuclear scattering to astrophysics.
• Time Series Analysis and Causal Dynamics in Stochastic Systems (7.3%) — This cluster analyzes time series data to infer stochastic model parameters, detect temporal asymmetry, and quantify multifractality and causal dynamics in systems such as financial markets and climate data.
• Quantum-Inspired Machine Learning and Entanglement Characterization (5.7%) — This cluster explores quantum entanglement, quantum critical phenomena, and quantum-inspired algorithms, often using machine learning to characterize quantum states and improve sensing.

Each sub-direction is covered across three chapters — how it framed its questions, the strength of its key findings, and its open debates and frontiers — so the reader gets a traceable picture of what this part of the field actually produced over the year.