统计应用：2025–2026 年度综述

An annual survey of the stat.AP arXiv category, covering research published from September 2025 – August 2026. Built on a close-reading set of 132 papers and organised into 37 chapters, it maps the year by the field's research sub-directions.

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

• Bayesian Spatial-Temporal Modeling for Epidemiology and Markets (58.8%) — Applies Bayesian hierarchical models and MCMC to quantify uncertainty in spatial-temporal dynamics of disease spread and market valuations.
• Robust Pattern Detection in Complex Environmental and Financial Systems (13.5%) — Focuses on monitoring and detecting anomalies or structural changes in high-dimensional datasets from environmental, financial, and social domains.
• Causal Inference and Statistical Estimation in Applied Sciences (11.8%) — Develops methods for estimating treatment effects and causal parameters in observational data across physics, medicine, and economics.
• Dynamic Risk Assessment and Adaptive Machine Learning (6.1%) — Utilizes dynamic modeling and machine learning to assess risks and optimize responses in evolving systems like healthcare and autonomous driving.
• Multivariate Time Series and Survival Analysis in Health and Environment (3.5%) — Analyzes temporal dependencies and survival rates in health, environmental, and astronomical time series data using advanced stochastic processes.
• Clinical Trial Design and Real-World Evidence Methodologies (2.6%) — Addresses challenges in designing and analyzing clinical trials, including digital twins and online experimentation, to improve real-world applicability.
• Evaluation and Robustness of Large Language Models (1.4%) — Investigates methods for evaluating LLM performance, robustness, and integration into scientific and data-fitting workflows.
• Policy Evaluation and Public Health Intervention Analysis (1.3%) — Evaluates the impact of public health and social policies using causal inference and explainable AI to address societal challenges.
• Probabilistic Modeling in Sports Analytics and Specialized Domains (0.5%) — Applies probabilistic strategies and distribution modeling to analyze outcomes in sports, soil health, and specialized statistical tests.
• Statistical Testing and Measurement Validity in Applied Contexts (0.3%) — Focuses on developing and refining statistical tests and measurement standards for validity in diverse applied settings like AI and medicine.
• Statistical Insights for Complex Interactions and Information Systems (0.2%) — Provides statistical frameworks for understanding complex interactions and optimizing information systems in marketplaces and biological contexts.

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.