This paper introduces a novel sequential inferential approach for Bayesian dynamic generalized linear models, focusing on uni- or multivariate k-parametric exponential families, which handle various responses such as multinomial, gamma, normal, and Poisson. This approach preserves the sequential nature of Bayesian paradigm for generating real-time inferences, utilizing the conjugate structure of the exponential family for computational efficiency. The framework incorporates concepts from Information Geometry, like the projection theorem and Kullback-Leibler divergence, aligning it with recent advancements in variational inference. Applications on artificial and real data demonstrate its computational efficiency. For instance, fitting and forecasting a stochastic volatility model took just 0.517s for a time series of 500 returns, outperforming alternative methods. The proposed approach accommodates new information strategically, enabling monitoring, intervention analyses, and the use of discount factors typical in sequential analyses. An R package is in development, with specific cases of k-parametric dynamic generalized models already implemented and available for direct use by applied researchers.

翻译：本文提出了一种新颖的贝叶斯动态广义线性模型序贯推断方法，聚焦于处理多项分布、伽马分布、正态分布和泊松分布等多元响应的单变量或多变量k-参数指数族。该方法保留了贝叶斯范式的序贯特性以生成实时推断，并利用指数族的共轭结构实现计算高效性。框架融入了信息几何中的投影定理与Kullback-Leibler散度等概念，与变分推断领域的最新进展相契合。在人工与真实数据上的应用验证了其计算效率：例如，对500个收益率时间序列进行随机波动率模型拟合与预测仅需0.517秒，优于其他对比方法。所提方法能够战略性地吸纳新信息，支持监控、干预分析以及序贯分析中典型的折扣因子使用。目前正在开发相应的R语言程序包，其中k-参数动态广义模型的特例已实现并可被应用研究者直接使用。