AI 中文总结
针对计量经济学等领域数据带来的挑战，引入基于INLA方法、用R-INLA软件实现的分布式递归推理贝叶斯框架，通过分区降低计算复杂度，经案例研究验证其有效性，为现代贝叶斯推理提供实用工具。
AI 中文摘要
计量经济学、环境科学、风险管理和公共政策等领域中大规模复杂数据集的快速增长重塑了统计建模，带来计算和方法上的重大挑战。这些挑战源于数据规模、模型复杂性、现代应用的顺序或流性质以及数据隐私限制。为应对这些挑战，我们引入了一种基于集成嵌套拉普拉斯近似（INLA）方法并使用R-INLA软件实现的新颖且全面的分布式递归推理贝叶斯框架。我们的贡献包括对数据和结构化模型组件进行分区，降低计算复杂性同时保持相对于集中式全数据推理的准确性。通过案例研究证明了该框架的有效性，突出了其在大规模、流和隐私敏感设置中的适用性。通过整合分布式、联邦和递归范式，这项工作为现代贝叶斯推理提供了可扩展、自适应和可推广的工具。
英文摘要
The rapid growth of massive and complex datasets in fields such as econometrics, environmental sciences, risk management, and public policy has reshaped statistical modeling while introducing significant computational and methodological challenges. These challenges arise not only from data scale and model complexity, but also from the sequential or streaming nature of modern applications and from data-privacy constraints that prevent sharing raw data and thus limit joint analysis. To address these challenges, we introduce a novel and comprehensive Bayesian framework for distributed and recursive inference, grounded in the Integrated Nested Laplace Approximations (INLA) methodology and implemented using the R-INLA software. Our contributions include the partitioning both data and structured model components, reducing computational complexity while preserving accuracy relative to centralized full-data inference. We demonstrate the effectiveness of the proposed framework through case studies that highlight its applicability in large-scale, streaming, and privacy-sensitive settings. By integrating distributed, federated, and recursive paradigms, this work offers scalable, adaptive, and generalizable tools for modern Bayesian inference.
Comments42 pages and 13 figures
