高维多类型响应的潜在多变量Log-Gamma模型及其在每日细颗粒物和死亡计数中的应用
Latent Multivariate Log-Gamma Models for High-Dimensional Multi-Type Responses with Application to Daily Fine Particulate Matter and Mortality Counts
摘要：
跟踪和估计每日细颗粒物（PM2.5）非常重要，因为已经表明PM2.5与肺部，心血管系统和中风相关的死亡率直接相关。也就是说，PM2.5的高值构成了美国的公共卫生问题，我们准确估计PM2.5以帮助公共政策决策是很重要的。因此，我们提出了一个贝叶斯层次模型的高维“多类型”的反应。“多类型”响应是指具有不同分布假设的相关响应的集合（例如，连续偏斜观测和计数值观测）。疾病控制和预防中心（CDC）数据库提供了与PM2.5和每日平均PM2.5相关的死亡率计数，这两者在我们的分析中均被视为响应。我们的模型利用了Weibull分布（对PM2.5建模）、Poisson分布（对疾病死亡率建模）和多变量对数Γ分布之间共享的共轭结构，并且我们使用降维来辅助计算。我们的模型也可以用来提高精度的估计和估计值在未披露/失踪的县。我们提供了一个模拟研究来说明模型的性能，并给出了CDC数据集的深入分析。
英文摘要：
Tracking and estimating Daily Fine Particulate Matter (PM2.5) is very important as it has been shown that PM2.5 is directly related to mortality related to lungs, cardiovascular system, and stroke. That is, high values of PM2.5 constitute a public health problem in the US, and it is important that we precisely estimate PM2.5 to aid in public policy decisions. Thus, we propose a Bayesian hierarchical model for high-dimensional "multi-type" responses. By "multi-type" responses we mean a collection of correlated responses that have different distributional assumptions (e.g., continuous skewed observations, and count-valued observations). The Centers for Disease Control and Prevention (CDC) database provides counts of mortalities related to PM2.5 and daily averaged PM2.5 which are both treated as responses in our analysis. Our model capitalizes on the shared conjugate structure between the Weibull (to model PM2.5), Poisson (to model diseases mortalities), and multivariate log-gamma distributions, and we use dimension reduction to aid with computation. Our model can also be used to improve the precision of estimates and estimate values at undisclosed/missing counties. We provide a simulation study to illustrate the performance of the model, and give an in-depth analysis of the CDC dataset.
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