Spatial stochastic volatility for lattice data
Spatial stochastic volatility for lattice data
复制标题
晶格数据的空间随机波动性
DOI：
10.1198/108571107x178068
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Jun Yan
中科院分区：
文献类型：
--
作者：
Jun Yan
空间异方差可能会出现联合空间自相关的格点数据收集农业试验和环境研究。这导致空间聚类不仅在水平上，而且在数据的变化，后者可能是非常重要的，例如，在构建预测区间。本文在广泛应用的条件自回归（CAR）模型中引入空间随机波动（SSV）成分，以捕捉异方差的空间聚集性。SSV分量是一个均值为零、条件独立的高斯过程，给出了方差的潜在空间过程。潜方差过程的对数由一个固有的高斯马尔可夫随机场指定。SSV模型放宽了传统空间异质性的同方差假设，为流行的空间统计模型带来了更大的灵活性。贝叶斯方法用于推理。异方差分量的全条件分布可以被证明是对数凹的，这有利于自适应拒绝抽样算法。著名的小麦产量数据的应用表明，将空间随机波动可能会揭示隐藏在现有的分析空间异方差。
Spatial heteroscedasticity may arise jointly with spatial autocorrelation in lattice data collected from agricultural trials and environmental studies. This leads to spatial clustering not only in the level but also in the variation of the data, the latter of which may be very important, for example, in constructing prediction intervals. This article introduces a spatial stochastic volatility (SSV) component into the widely used conditional autoregressive (CAR) model to capture the spatial clustering in heteroscedasticity. The SSV component is a mean zero, conditionally independent Gaussian process given a latent spatial process of the variances. The logarithm of the latent variance process is specified by an intrinsic Gaussian Markov random field. The SSV model relaxes the traditional homoscedasticity assumption for spatial heterogeneity and brings greater flexibility to the popular spatial statistical models. The Bayesian method is used for inference. The full conditional distribution of the heteroscedasticity components can be shown to be log-concave, which facilitates an adaptive rejection sampling algorithm. Application to the well-known wheat yield data illustrates that incorporating spatial stochastic volatility may reveal the spatial heteroscedasticity hidden from existing analyses.