评价Besag-York-Mollié CAR模型的信息性
Evaluating the Informativeness of the Besag-York-Mollié CAR Model
摘要：
Besag，York和Mollié（1991; BYM）提出的条件自回归框架的使用在贝叶斯疾病制图和空间流行病学中无处不在。虽然应当理解，贝叶斯推断基于数据中包含的信息和模型贡献的信息的组合，但是相对于数据中的信息量化模型的贡献通常是不平凡的。在这里，我们提供了一个衡量的贡献的BYM框架，首先考虑简单的泊松-伽马设置，量化先验的贡献是相当清楚的。然后，我们提出了伽马和对数正态先验之间的关系，我们然后扩展到涵盖BYM提出的框架。在一个简短的模拟研究中，我们说明了我们的伽马先验的对数正态近似的准确性，我们分析了一个数据集，包括县级心脏病相关的死亡数据在美国各地。除了证明BYM框架对应于高度信息化的先验规范的潜力之外，我们还说明了死亡率估计对BYM框架信息性变化的敏感性。
英文摘要：
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.
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