Dynamic generalized linear models may be seen simultaneously as an extension to dynamic linear models and to generalized linear models, formally treating serial auto-correlation inherent to responses observed through time. The present work revisits inference methods for this class, proposing an approach based on information geometry, focusing on the $k$- parametric exponential family. Among others, the proposed method accommodates multinomial and can be adapted to accommodate compositional responses on $k=d+1$ categories, while preserving the sequential aspect of the Bayesian inferential procedure, producing real-time inference. The updating scheme benefits from the conjugate structure in the exponential family, assuring computational efficiency. Concepts such as Kullback-Leibler divergence and the projection theorem are used in the development of the method, placing it close to recent approaches on variational inference. Applications to real data are presented, demonstrating the computational efficiency of the method, favorably comparing to alternative approaches, as well as its flexibility to quickly accommodate new information when strategically needed, preserving aspects of monitoring and intervention analysis, as well as discount factors, which are usual in sequential analyzes.

翻译：动态广义线性模型可同时视为动态线性模型与广义线性模型的扩展，形式化地处理观测序列中固有的时间序列自相关性。本文重新审视此类模型的推断方法，提出一种基于信息几何的新方法，重点研究$k$参数指数族分布。该方法不仅能处理多项分布，还可适配$k=d+1$个类别的成分响应数据，同时保持贝叶斯推断过程的序贯特性，实现实时推断。其更新机制利用指数族分布的共轭结构，确保计算效率。通过运用Kullback-Leibler散度与投影定理等概念，该方法与近年来的变分推断方法紧密关联。本文通过实际数据应用，展示了该方法在计算效率上的优势（优于其他对比方法），以及在需要时快速整合新信息的灵活性，同时保留了序贯分析中常用的监测分析、干预分析和折扣因子等特征。