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Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models

机译:空间广义线性混合模型中的近似贝叶斯推断

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In this paper we propose fast approximate methods for computing posterior marginals in spatial generalized linear mixed models. We consider the common geostatistical case with a high dimensional latent spatial variable and observations at known registration sites. The methods of inference are deterministic, using no simulation-based inference. The first proposed approximation is fast to compute and is 'practically sufficient', meaning that results do not show any bias or dispersion effects that might affect decision making. Our second approximation, an improvement of the first version, is 'practically exact', meaning that one would have to run MCMC simulations for very much longer than is typically done to detect any indication of error in the approximate results. For small-count data the approximations are slightly worse, but still very accurate. Our methods are limited to likelihood functions that give unimodal full conditionals for the latent variable. The methods help to expand the future scope of non-Gaussian geostatistical models as illustrated by applications of model choice, outlier detection and sampling design. The approximations take seconds or minutes of CPU time, in sharp contrast to overnight MCMC runs for solving such problems.
机译:在本文中,我们提出了一种用于空间广义线性混合模型中计算后边际的快速近似方法。我们考虑具有高维潜在空间变量的常见地统计学情况,并在已知的注册地点进行观测。推理方法是确定性的,不使用基于模拟的推理。提出的第一个近似值计算速度快,并且“实际上足够”,这意味着结果不会显示任何可能影响决策的偏见或分散效应。我们的第二个近似值是对第一个版本的改进,“实际上是精确的”,这意味着必须将MCMC模拟运行的时间比检测近似结果中任何错误指示的典型运行时间长得多。对于小数量的数据,近似值稍差一些,但仍然非常准确。我们的方法仅限于为潜在变量提供单峰完全条件的似然函数。这些方法有助于扩大非高斯地统计模型的未来范围,如模型选择,离群值检测和采样设计的应用所示。近似值需要花费几秒钟或几分钟的CPU时间,与整夜为解决此类问题而运行的MCMC形成鲜明对比。

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