Approximating likelihoods for large spatial data sets
Approximating likelihoods for large spatial data sets
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DOI：
10.1046/j.1369-7412.2003.05512.x
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发表时间：
2004-01-01
影响因子：
5.8
通讯作者：
Welty, LJ
中科院分区：
文献类型：
--
作者：
Stein, ML;Chi, ZY;Welty, LJ
由于计算负担，似然方法通常难以用于大型、不规则定位的空间数据集。即使对于高斯模型，精确计算n个观测值的似然性也需要O（n（3））运算。由于任何联合密度都可以写为基于观测的某种排序的条件密度的乘积，因此减少计算的一种方法是在计算条件密度时仅以一些“过去”观测为条件。我们展示了这种方法可以适应近似的限制可能性，我们演示了如何估计方程的方法，使我们能够判断所得到的近似的功效。以前的工作建议条件反射那些过去的观察，最接近的观察，我们的条件密度近似。通过理论，数值和实际的例子，我们表明，往往可以有相当大的好处，在一些遥远的观测条件。
Likelihood methods are often difficult to use with large, irregularly sited spatial data sets, owing to the computational burden. Even for Gaussian models, exact calculations of the likelihood for n observations require O(n(3)) operations. Since any joint density can be written as a product of conditional densities based on some ordering of the observations, one way to lessen the computations is to condition on only some of the 'past' observations when computing the conditional densities. We show how this approach can be adapted to approximate the restricted likelihood and we demonstrate how an estimating equations approach allows us to judge the efficacy of the resulting approximation. Previous work has suggested conditioning on those past observations that are closest to the observation whose conditional density we are approximating. Through theoretical, numerical and practical examples, we show that there can often be considerable benefit in conditioning on some distant observations as well.