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 Pólya-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.

翻译：本文为泊松INGARCH模型开发了一种高效的后验抽样方案。所提方法基于对后验密度的近似，该近似利用了负二项分布的泊松极限特性。该方法允许我们将模型重写为适用于Pólya-Gamma数据增强方案的形式，从而为自回归系数提供了简单的条件高斯更新。通过吉布斯型迭代，从近似后验中抽样是直接可行的，即使在强时间依赖性下也能保持数值稳定性。将此抽样器用作建议分布将提高Metropolis-Hastings算法和自适应重要性抽样的效率。数值模拟表明，该方法能获得准确的后验估计、较高的有效样本量以及快速混合的马尔可夫链。