论文标题
评估Besag-York-Mollié汽车模型的信息性
Evaluating the Informativeness of the Besag-York-Mollié CAR Model
论文作者
论文摘要
Besag，York和Mollié（1991; Bym）提出的条件自回旋框架的使用在贝叶斯病映射和空间流行病学中无处不在。虽然据了解，贝叶斯推论是基于数据中包含的信息和模型贡献的信息的组合，量化模型相对于数据中信息的贡献通常是不平凡的。在这里，我们首先考虑了简单的泊松式伽马设置，从而提供了BYM框架的贡献，在这种情况下，量化了先验的贡献非常清楚。然后，我们提出了伽马和log态先验之间的关系，然后扩展到涵盖BYM提出的框架。经过一项简短的仿真研究，我们说明了伽玛之前的对数正态近似的准确性，我们分析了一个由美国县级心脏病相关的死亡数据组成的数据集。除了证明BYM框架对应于高度信息的先验规范的潜力外，我们还说明了死亡率估计对BYM框架信息变化的敏感性。
The use of the conditional autoregressive framework proposed by Besag, York, and Mollié (1991; BYM) is ubiquitous in Bayesian disease mapping and spatial epidemiology. While it is understood that Bayesian inference is based on a combination of the information contained in the data and the information contributed by the model, quantifying the contribution of the model relative to the information in the data is often non-trivial. Here, we provide a measure of the contribution of the BYM framework by first considering the simple Poisson-gamma setting in which quantifying the prior's contribution is quite clear. We then propose a relationship between gamma and lognormal priors that we then extend to cover the framework proposed by BYM. Following a brief simulation study in which we illustrate the accuracy of our lognormal approximation of the gamma prior, we analyze a dataset comprised of county-level heart disease-related death data across the United States. In addition to demonstrating the potential for the BYM framework to correspond to a highly informative prior specification, we also illustrate the sensitivity of death rate estimates to changes in the informativeness of the BYM framework.
