k-parametric Dynamic Generalized Linear Models: a sequential approach via Information Geometry

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.