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Hierarchical Bayesian autoregressive models for large space-time data with applications to ozone concentration modelling

机译：大型时空数据的分层贝叶斯自回归模型及其在臭氧浓度建模中的应用

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摘要

Increasingly large volumes of space-time data are collected everywhere by mobile computing applications, and in many of these cases, temporal data are obtained by registering events, for example, telecommunication or Web traffic data. Having both the spatial and temporal dimensions adds substantial complexity to data analysis and inference tasks. The computational complexity increases rapidly for fitting Bayesian hierarchical models, as such a task involves repeated inversion of large matrices. The primary focus of this paper is on developing space-time autoregressive models under the hierarchical Bayesian setup. To handle large data sets, a recently developed Gaussian predictive process approximation method is extended to include autoregressive terms of latent space-time processes. Specifically, a space-time autoregressive process, supported on a set of a smaller number of knot locations, is spatially interpolated to approximate the original space-time process. The resulting model is specified within a hierarchical Bayesian framework, and Markov chain Monte Carlo techniques are used to make inference. The proposed model is applied for analysing the daily maximum 8-h average ground level ozone concentration data from 1997 to 2006 from a large study region in the Eastern United States. The developed methods allow accurate spatial prediction of a temporally aggregated ozone summary, known as the primary ozone standard, along with its uncertainty, at any unmonitored location during the study period. Trends in spatial patterns of many features of the posterior predictive distribution of the primary standard, such as the probability of noncompliance with respect to the standard, are obtained and illustrated.
机译：越来越多的时空数据被移动计算应用程序收集到各处，并且在许多情况下，通过注册事件（例如，电信或Web流量数据）来获得时间数据。同时具有空间和时间维度会大大增加数据分析和推理任务的复杂性。拟合贝叶斯层次模型的计算复杂度迅速增加，因为这样的任务涉及大矩阵的反复反演。本文的主要重点是在分层贝叶斯设置下开发时空自回归模型。为了处理大型数据集，最近开发的高斯预测过程近似方法得到扩展，以包括潜在时空过程的自回归项。具体而言，对一组较少数量的结位置上支持的时空自回归过程进行空间插值，以近似原始时空过程。结果模型在分层贝叶斯框架内指定，并且使用马尔可夫链蒙特卡洛技术进行推理。所提出的模型用于分析美国东部一个大型研究区从1997年到2006年的每日最大8小时平均地面臭氧浓度数据。所开发的方法可以在研究期间的任何不受监视的位置，对称为时间基准的臭氧总汇以及其不确定性进行精确的空间预测。获得并说明了主要标准的后验预测分布的许多特征的空间模式趋势，例如相对于标准的不符合概率。

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