An efficient method of posterior sampling for Poisson INGARCH models

2026-03-08

AI Summary

This study addresses the challenges of low posterior sampling efficiency and numerical instability in Poisson INGARCH models under strong temporal dependence. To overcome these issues, the authors introduce Pólya–Gamma data augmentation for the first time, leveraging a Poisson limit approximation of the negative binomial distribution to recast the posterior into a conditionally Gaussian form. This reformulation enables efficient Gibbs updates for autoregressive coefficients. The proposed method not only yields a stable approximate posterior suitable for strongly dependent settings but also serves as a high-quality proposal distribution for Metropolis–Hastings algorithms and adaptive importance sampling. Numerical experiments demonstrate that the approach substantially improves sampling efficiency, effective sample size, and chain mixing speed while maintaining accurate posterior inference.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We develop an efficient posterior sampling scheme for the Poisson INGARCH models. The proposed method is based on the approximation of the posterior density that exploits the Poisson limit of the negative binomial distribution. It allows us to rewrite the model in a form amenable to P\'olya-Gamma data augmentation scheme, which yields simple conditionally Gaussian updates for the autoregressive coefficients. Sampling from the approximate posterior is straightforward via Gibbs-type iterations and remains numerically stable even under strong temporal dependence. Using this sampler as a proposal distribution will enhance the efficiency in Metropolis-Hastings algorithm and adaptive importance sampling. Numerical simulations indicate accurate posterior estimates, high effective sample sizes, and rapidly mixing chains.

Problem

• posterior sampling
• Poisson INGARCH
• Markov chain Monte Carlo
• temporal dependence
• Bayesian inference

Innovation

• Poisson INGARCH
• Pólya-Gamma augmentation
• posterior sampling
• negative binomial approximation
• Gibbs sampling