On data augmentation for models involving reciprocal gamma functions
On data augmentation for models involving reciprocal gamma functions
复制标题
关于涉及倒伽玛函数的模型的数据增强
DOI：
10.1080/10618600.2022.2119988
复制
发表时间：
2022
影响因子：
2.4
通讯作者：
Sugasawa Shonosuke
中科院分区：
文献类型：
--
作者：
Hamura Yasuyuki;Irie Kaoru;Sugasawa Shonosuke
在这篇文章中，我们介绍了一种新的和有效的数据增强方法的形状参数模型的后验推断时，倒易伽玛函数出现在全条件密度。我们的方法是通过使用高斯的乘法公式和斯特林公式的伽玛函数，其中的近似误差可以任意小的形状参数的全条件密度。我们使用的技术来构建有效的吉布斯和大都会黑斯廷斯算法的各种模型，涉及伽玛分布，学生的st分布，狄利克雷分布，负二项分布，和Wishart分布。所提出的采样方法是通过模拟研究数值证明。本文的补充材料可在网上查阅。
In this article, we introduce a new and efficient data augmentation approach to the posterior inference of the models with shape parameters when the reciprocal gamma function appears in full conditional densities. Our approach is to approximate full conditional densities of shape parameters by using Gauss’s multiplication formula and Stirling’s formula for the gamma function, where the approximation error can be made arbitrarily small. We use the techniques to construct efficient Gibbs and Metropolis–Hastings algorithms for a variety of models that involve the gamma distribution, Student’st-distribution, the Dirichlet distribution, the negative binomial distribution, and the Wishart distribution. The proposed sampling method is numerically demonstrated through simulation studies. Supplementary materials for this article are available online.