论文标题
具有多分辨率近似的时空数据的完全贝叶斯推断
Fully Bayesian inference for spatiotemporal data with the multi-resolution approximation
论文作者
论文摘要
大型时空数据集是常规贝叶斯模型的挑战，因为算法在多变量正常密度中获得协方差矩阵的Cholesky分解的立方计算复杂性。此外，在这种情况下，用于后验估计的标准数值算法，例如马尔可夫链蒙特卡洛（MCMC），在这种情况下非常棘手，因为它们需要数千（即使不是数百万）的可能性评估。为了克服这些局限性，我们提出了IS-MRA（重要性采样 - 多分辨率近似），它利用了由多分辨率近似（MRA）方法产生的稀疏逆协方差结构。 IS-MRA是完全贝叶斯的，并促进了高参数边缘后部分布的近似。我们将IS-MRA应用于大型MODIS 3级地表温度（LST）数据集，并在2012年5月18日至5月31日在印度马哈拉施特拉邦的西部进行了采样。我们发现，IS-MRA可以在观察到大量云覆盖引起的集中遗失的区域上产生现实的预测表面。通过验证分析和仿真研究，我们还发现预测往往非常准确。
Large spatiotemporal datasets are a challenge for conventional Bayesian models because of the cubic computational complexity of the algorithms for obtaining the Cholesky decomposition of the covariance matrix in the multivariate normal density. Moreover, standard numerical algorithms for posterior estimation, such as Markov Chain Monte Carlo (MCMC), are intractable in this context, as they require thousands, if not millions, of costly likelihood evaluations. To overcome those limitations, we propose IS-MRA (Importance sampling - Multi-Resolution Approximation), which takes advantage of the sparse inverse covariance structure produced by the Multi-Resolution Approximation (MRA) approach. IS-MRA is fully Bayesian and facilitates the approximation of the hyperparameter marginal posterior distributions. We apply IS-MRA to large MODIS Level 3 Land Surface Temperature (LST) datasets, sampled between May 18 and May 31, 2012 in the western part of the state of Maharashtra, India. We find that IS-MRA can produce realistic prediction surfaces over regions where concentrated missingness, caused by sizable cloud cover, is observed. Through a validation analysis and simulation study, we also find that predictions tend to be very accurate.
