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Restricted Covariance Priors with Applications in Spatial Statistics

机译:受限协方差先验及其在空间统计中的应用

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摘要

We present a Bayesian model for area-level count data that uses Gaussian random effects with a novel type of G-Wishart prior on the inverse variance– covariance matrix. Specifically, we introduce a new distribution called the truncated G-Wishart distribution that has support over precision matrices that lead to positive associations between the random effects of neighboring regions while preserving conditional independence of non-neighboring regions. We describe Markov chain Monte Carlo sampling algorithms for the truncated G-Wishart prior in a disease mapping context and compare our results to Bayesian hierarchical models based on intrinsic autoregression priors. A simulation study illustrates that using the truncated G-Wishart prior improves over the intrinsic autoregressive priors when there are discontinuities in the disease risk surface. The new model is applied to an analysis of cancer incidence data in Washington State.
机译:我们提出了一个区域面积计数数据的贝叶斯模型,该模型在逆方差-协方差矩阵上使用了具有新型G-Wishart的高斯随机效应。具体而言,我们引入了一种称为截断G-Wishart分布的新分布,该分布对精度矩阵提供了支持,该精度矩阵导致相邻区域的随机效应之间存在正关联,同时保留了非相邻区域的条件独立性。我们在疾病映射环境中描述了截短的G-Wishart先验的Markov链蒙特卡罗采样算法,并将我们的结果与基于固有自回归先验的贝叶斯层次模型进行比较。模拟研究表明,当疾病风险面不连续时,使用截断的G-Wishart先验比固有的自回归先验有改进。新模型用于华盛顿州癌症发病率数据的分析。

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