On conditional and intrinsic autoregressions
On conditional and intrinsic autoregressions
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DOI：
10.2307/2337341
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发表时间：
1995-12-01
期刊：
影响因子：
2.7
通讯作者：
Kooperberg, C
中科院分区：
文献类型：
--
作者：
Besag, J;Kooperberg, C
高斯条件自回归已广泛应用于空间统计和贝叶斯图像分析，其目的是描述欧几里德空间中固定位置的随机变量之间的相互作用。这些分布的主要吸引力在于其完整条件的马尔可夫解释。内在自回归是保留马尔可夫性质的限制形式。尽管不合适，但它们在概念上和实践上都比标准自回归具有优势。例如，它们通常避免参数估计中的困难，而没有明显的损失，或者表现出吸引人的不变性，如纹理分析。然而，在小型阵列和非晶格应用中，两种形式的自回归都可能导致不期望的二阶特性，无论是在变量本身还是在变量之间的对比中。本文讨论了标准和内在自回归，并描述了如何使用 Dempster (1972) 算法或适当的修改来缓解所出现的问题。该方法代表了标准地统计和高斯马尔可夫随机场公式的部分综合。还提到了一些非空间应用。
Gaussian conditional autoregressions have been widely used in spatial statistics and Bayesian image analysis, where they are intended to describe interactions between random variables at fixed sites in Euclidean space. The main appeal of these distributions is in the Markovian interpretation of their full conditionals. Intrinsic autoregressions are limiting forms that retain the Markov property. Despite being improper, they can have advantages over the standard autoregressions, both conceptually and in practice. For example, they often avoid difficulties in parameter estimation, without apparent loss, or exhibit appealing invariances, as in texture analysis. However, on small arrays and in nonlattice applications, both forms of autoregression can lead to undesirable second-order characteristics, either in the variables themselves or in contrasts among them. This paper discusses standard and intrinsic autoregressions and describes how the problems that arise can be alleviated using Dempster's (1972) algorithm or an appropriate modification. The approach represents a partial synthesis of standard geostatistical and Gaussian Markov random field formulations. Some nonspatial applications are also mentioned.