Poisson log-linear models are ubiquitous in many applications, and one of the most popular approaches for parametric count regression. In the Bayesian context, however, there are no sufficient specific computational tools for efficient sampling from the posterior distribution of parameters, and standard algorithms, such as random walk Metropolis-Hastings or Hamiltonian Monte Carlo algorithms, are typically used. Herein, we developed an efficient Metropolis-Hastings algorithm and importance sampler to simulate from the posterior distribution of the parameters of Poisson log-linear models under conditional Gaussian priors with superior performance with respect to the state-of-the-art alternatives. The key for both algorithms is the introduction of a proposal density based on a Gaussian approximation of the posterior distribution of parameters. Specifically, our result leverages the negative binomial approximation of the Poisson likelihood and the successful P\'olya-gamma data augmentation scheme. Via simulation, we obtained that the time per independent sample of the proposed samplers is competitive with that obtained using the successful Hamiltonian Monte Carlo sampling, with the Metropolis-Hastings showing superior performance in all scenarios considered.

翻译：Poisson log- 线性模型在许多应用中普遍存在,也是最受欢迎的参数计数回归方法之一。然而,在巴伊西亚,没有足够具体的计算工具从参数的后座分布中有效取样,而且通常使用标准算法,例如随机步行大都会分布法或汉密尔顿蒙特卡洛算法。在这里,我们开发了高效的大都会- 开发算法和重要取样器,以模拟在条件性高山前台下Poisson log- 线性模型参数的后座分布,在最新替代技术方面表现优异。这两种算法的关键是引入基于参数后座分布高斯近似戈斯的推荐密度。具体地说,我们的结果利用Poisson可能性和成功的P\'olya- gamma数据增强办法的负双波近似近似近似近似值。Via模拟,我们获得的拟议取样员在使用汉密尔顿- 蒙特卡罗斯所有设想的高级模拟方案所取得的竞争力。