统计计算：2025–2026 年度综述

An annual survey of the stat.CO arXiv category, covering research published from September 2025 – August 2026. Built on a close-reading set of 100 papers and organised into 28 chapters, it maps the year by the field's research sub-directions.

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

• High-Performance Bayesian Inference and Uncertainty Quantification (87.2%) — Focuses on scalable algorithms, GPU acceleration, and specialized sampling techniques for high-dimensional models and complex data structures.
• Advanced Markov Chain Monte Carlo and Sampling Algorithms (10.2%) — Develops novel MCMC, Hamiltonian Monte Carlo, and ensemble samplers to improve efficiency and accuracy in posterior estimation.
• Stochastic Optimization and Differential Equation Solvers (1.3%) — Addresses theoretical guarantees and numerical methods for stochastic gradient descent, Langevin dynamics, and inverse problems in dynamic systems.
• Flexible Regression Models and Distributional Learning (0.9%) — Explores generalized, neural, and robust regression techniques for handling complex response types, outliers, and non-standard data structures.
• Deep Learning Integration for Statistical Inference (0.3%) — Investigates the intersection of deep learning and statistical inference, including conformal prediction and simulation-based inference.
• Robust Statistical Methods for Outlier Detection (0.1%) — Examines robust regression and outlier detection techniques, specifically addressing missing values and cellwise anomalies.

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.