An Efficient Sequential Approach for k-Parametric Dynamic Generalised Linear Models

TL;DR

This paper introduces a new efficient sequential Bayesian inference method for k-parametric dynamic generalized linear models, capable of handling diverse data types with improved computational performance and scalability.

Contribution

It presents a novel sequential inferential approach that leverages information geometry and conjugate structures for dynamic GLMs across multiple exponential family distributions.

Findings

Demonstrates computational efficiency and scalability on synthetic and real datasets.

Outperforms existing methods in speed and accuracy.

Provides an accessible R package for practical implementation.

Abstract

A novel sequential inferential method for Bayesian dynamic generalised linear models is presented, addressing both univariate and multivariate $k$-parametric exponential families. It efficiently handles diverse responses, including multinomial, gamma, normal, and Poisson distributed outcomes, by leveraging the conjugate and predictive structure of the exponential family. The approach integrates information geometry concepts, such as the projection theorem and Kullback-Leibler divergence, and aligns with recent advances in variational inference. Applications to both synthetic and real datasets highlight its computational efficiency and scalability, surpassing alternative methods. The approach supports the strategic integration of new information, facilitating monitoring, intervention, and the application of discount factors, which are typical in sequential analyses. The R package kDGLM is available for direct use by applied researchers, facilitating the implementation of the method for specific k-parametric dynamic generalised models.