An h-likelihood method for spatial mixed linear models based on intrinsic auto-regressions
An h-likelihood method for spatial mixed linear models based on intrinsic auto-regressions
复制标题
DOI：
10.1111/rssb.12084
复制
发表时间：
2015-06-01
影响因子：
5.8
通讯作者：
Mondal, Debashis
中科院分区：
文献类型：
--
作者：
Dutta, Somak;Mondal, Debashis
我们考虑稀疏空间混合线性模型，特别是 Besag 和 Higdon 描述的模型，并为其统计推断开发一种 h 似然方法。所提出的方法允许奇异精度矩阵，因为它产生的估计与基于数据的适当差分的剩余最大似然的估计一致，并且具有通过伽玛线性模型估计精度参数的新颖方法。此外，我们通过明确使用规则数组上的高斯内马尔可夫随机场和 de Wijs 过程之间的缩放限制连接，将 h 似然方法推广到包括连续空间变化。考虑到空间混合线性模型的各种应用，我们设计了一种新颖的稀疏共轭梯度算法，使我们能够实现快速的无矩阵统计计算。我们提供两种应用程序。第一个是对农业品种试验的广泛分析，提出了最近邻调整的各种新方面，例如对规模变化的统计分析的影响以及隐式连续空间公式的使用。第二个应用涉及对大棉田的分析，重点关注无矩阵计算。本文最后提出了一些进一步的考虑，例如对不规则间隔数据的应用、参数引导程序的使用以及对高斯马特恩混合效应模型的一些概括。
We consider sparse spatial mixed linear models, particularly those described by Besag and Higdon, and develop an h-likelihood method for their statistical inference. The method proposed allows for singular precision matrices, as it produces estimates that coincide with those from the residual maximum likelihood based on appropriate differencing of the data and has a novel approach to estimating precision parameters by a gamma linear model. Furthermore, we generalize the h-likelihood method to include continuum spatial variations by making explicit use of scaling limit connections between Gaussian intrinsic Markov random fields on regular arrays and the de Wijs process. Keeping various applications of spatial mixed linear models in mind, we devise a novel sparse conjugate gradient algorithm that allows us to achieve fast matrix-free statistical computations. We provide two applications. The first is an extensive analysis of an agricultural variety trial that brings forward various new aspects of nearest neighbour adjustment such as effects on statistical analyses to changes of scale and use of implicit continuum spatial formulation. The second application concerns an analysis of a large cotton field which gives a focus to matrix-free computations. The paper closes with some further considerations, such as applications to irregularly spaced data, use of the parametric bootstrap and some generalizations to the Gaussian Matern mixed effect models.