An efficient method of posterior sampling for Poisson INGARCH models

TL;DR

This paper introduces a computationally efficient posterior sampling method for Poisson INGARCH models, leveraging Poisson limits and Pólya-Gamma augmentation to improve stability and sampling efficiency.

Contribution

It presents a novel sampling scheme that simplifies posterior inference for Poisson INGARCH models using Pólya-Gamma augmentation and approximate posterior densities.

Findings

Accurate posterior estimates demonstrated in simulations

High effective sample sizes achieved

Chains exhibit rapid mixing and numerical stability

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.