Towards useable models for complex spatial data

随着数据变得越来越大，模型变得越来越复杂，可用的统计工具也变得越来越难以应对。对于具有空间或时空成分的数据集尤其如此，这些数据集越来越多地在生态学、流行病学、大气科学、渔业科学和林业等不同领域收集。对于这些问题，不仅仅是计算方法无法适应现代数据。我们建立空间模型的方法也需要根据分析大数据集的优势和挑战进行重新思考。******提出的研究计划有三个主线。首先是扩展现有的大规模空间数据建模方法，以考虑不确定性的多个来源、设计问题和多层结构。第二部分着眼于为潜在高斯模型类指定和评估先验分布的一般问题，其中包括在第一个线程中作为特殊情况考虑的空间模型。第三个线程着眼于改进当前最先进的方法，用于这些类型的模型的快速贝叶斯计算。在其中，我们将特别关注用于近似贝叶斯推理的集成嵌套拉普拉斯近似（INLA）的扩展以及在Stan概率编程语言中实现的MCMC方法。这些进步将增加空间和时空模型的类别，这些模型可以常规地适用于大型数据集，同时将结果实现为应用统计学家和科学家使用的工具。* * * * *

As data gets bigger, models become more complex and the available statistical tools become less and less able to cope. This is particularly true for datasets with a spatial or spatiotemporal component, which are increasingly being collected in fields as diverse as ecology, epidemiology, atmospheric science, fisheries science, and forestry. For these problems, it is not just computational methods that are failing to scale to modern data. Our methods for building spatial models also need to be re-thought in light of both the advantages and challenges of analysing large data sets. ******The proposed programme of research has three main threads. The first is to extend existing methods of modelling large-scale spatial data to account for multiple sources of uncertainty, design issues, and multilevel structure. The second looks at the general problem of specifying and evaluating prior distributions for the class of latent Gaussian models, which includes the spatial models considered in the first thread as a special case. The third thread looks to improve the current state-of-the-art methods for fast Bayesian computing for these types of models. In it we will focus particularly on extensions of the Integrated Nested Laplace Approximation (INLA) for approximate Bayesian inference and the MCMC methods implemented in the Stan probabilistic programming language. These advances will increase the class of spatial and spatiotemporal models that can be routinely fit to large data sets, while implementing the outcomes in a tool that can be used by applied statisticians and scientists. *****