Variational Bayesian methods for spatial data analysis
Variational Bayesian methods for spatial data analysis
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DOI：
10.1016/j.csda.2011.05.021
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发表时间：
2011-12
期刊：
影响因子：
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通讯作者：
Q. Ren;Sudipto Banerjee;A. Finley;J. Hodges
中科院分区：
文献类型：
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作者：
Q. Ren;Sudipto Banerjee;A. Finley;J. Hodges
随着地理编码位置上可用的科学数据，研究人员越来越多地转向空间过程模型来进行统计推断。然而，拟合空间模型通常涉及昂贵的矩阵分解，其计算复杂度随着空间位置数量的增加而按三次方增加。这种情况在贝叶斯设置中更为严重，其中马尔可夫链蒙特卡罗 (MCMC) 算法的每次迭代都需要进行一次此类计算。在本文中，我们描述了使用变分贝叶斯 (VB) 方法作为 MCMC 的替代方法来近似复杂空间模型的后验分布。多年来在贝叶斯机器学习中广泛使用的变分方法提供了边际似然的下界，可以有效地计算。我们提供了几个模型中变分更新的结果，特别强调它们在多元空间分析中的使用。我们通过使用模拟数据和环境数据集来演示 VB 方法的估计和模型比较，并将它们与 MCMC 的推论进行比较。
With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. However, fitting spatial models often involves expensive matrix decompositions, whose computational complexity increases in cubic order with the number of spatial locations. This situation is aggravated in Bayesian settings where such computations are required once at every iteration of the Markov chain Monte Carlo (MCMC) algorithms. In this paper, we describe the use of Variational Bayesian (VB) methods as an alternative to MCMC to approximate the posterior distributions of complex spatial models. Variational methods, which have been used extensively in Bayesian machine learning for several years, provide a lower bound on the marginal likelihood, which can be computed efficiently. We provide results for the variational updates in several models especially emphasizing their use in multivariate spatial analysis. We demonstrate estimation and model comparisons from VB methods by using simulated data as well as environmental data sets and compare them with inference from MCMC.