Bayesian Hierarchical Models With Conjugate Full-Conditional Distributions for Dependent Data From the Natural Exponential Family
Bayesian Hierarchical Models With Conjugate Full-Conditional Distributions for Dependent Data From the Natural Exponential Family
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DOI：
10.1080/01621459.2019.1677471
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发表时间：
2019-11-22
影响因子：
3.7
通讯作者：
Wikle, Christopher K.
中科院分区：
文献类型：
--
作者：
Bradley, Jonathan R.;Holan, Scott H.;Wikle, Christopher K.
我们介绍了一种贝叶斯方法，用于分析（可能）高维相关数据，这些数据根据自然指数分布家族的成员分布。这个问题需要广泛的方法进步，因为联合建模高维相关数据会导致所谓的“大n问题”。当允许非高斯数据模型时，“大n问题”的计算复杂性进一步加剧，就像这里的情况一样。因此，我们开发了新的计算效率的分布理论，这种设置。特别是，我们引入了“共轭多元分布”，这是出于Diaconis和Ylvisaker分布。此外，我们提供了大量的理论和方法的发展，包括：条件分布的结果，与多元正态分布，共轭先验分布，和全条件分布的吉布斯采样器的渐近关系。为了证明所提出的方法的广泛适用性，我们提供了两个模拟研究和三个应用程序的基础上流行病学数据集，一个联邦统计数据集，和环境数据集，分别。可以在网上找到。
We introduce a Bayesian approach for analyzing (possibly) high-dimensional dependent data that are distributed according to a member from the natural exponential family of distributions. This problem requires extensive methodological advancements, as jointly modeling high-dimensional dependent data leads to the so-called "big n problem." The computational complexity of the "big n problem" is further exacerbated when allowing for non-Gaussian data models, as is the case here. Thus, we develop new computationally efficient distribution theory for this setting. In particular, we introduce the "conjugate multivariate distribution," which is motivated by the Diaconis and Ylvisaker distribution. Furthermore, we provide substantial theoretical and methodological development including: results regarding conditional distributions, an asymptotic relationship with the multivariate normal distribution, conjugate prior distributions, and full-conditional distributions for a Gibbs sampler. To demonstrate the wide-applicability of the proposed methodology, we provide two simulation studies and three applications based on an epidemiology dataset, a federal statistics dataset, and an environmental dataset, respectively. for this article are available online.