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Multi-scale process modelling and distributed computation for spatial data

机译：空间数据的多尺度过程建模和分布式计算

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摘要

Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that modelling and prediction using infinite-dimensional process models is not possible with large data sets, and that both approximate models and, often, approximate-inference methods, are needed. The problem of fitting simple global spatial models to large data sets has been solved through the likes of multi-resolution approximations and nearest-neighbour techniques. Here we tackle the next challenge, that of fitting complex, nonstationary, multi-scale models to large data sets. We propose doing this through the use of superpositions of spatial processes with increasing spatial scale and increasing degrees of nonstationarity. Computation is facilitated through the use of Gaussian Markov random fields and parallel Markov chain Monte Carlo based on graph colouring. The resulting model allows for both distributed computing and distributed data. Importantly, it provides opportunities for genuine model and data scalability and yet is still able to borrow strength across large spatial scales. We illustrate a two-scale version on a data set of sea-surface temperature containing on the order of one million observations, and compare our approach to state-of-the-art spatial modelling and prediction methods.
机译：近年来在空间建模和预测方法中看到了巨大的发展，通过增加遥感数据的可用性以及分布式处理技术的成本降低的推动。众所周知，使用大数据集不可能使用无限维过程模型的建模和预测，并且需要近似模型和通常，近似推理方法。通过多分辨率近似和最近邻的技术来解决拟合简单的全局空间模型到大数据集的问题。在这里，我们解决了拟合复杂，非间平，多尺度模型到大数据集的下一个挑战。我们提出通过使用空间过程的叠加来实现这一目标，随着空间尺度的增加和不断增加的非间抗性。通过使用Gaussian Markov随机字段和基于图形着色的并行马尔可夫链Monte Carlo来促进计算。结果模型允许分布式计算和分布式数据。重要的是，它为真正的模型和数据可扩展性提供了机会，但仍然能够在大型空间尺度上借用实力。我们在含有一百万个观察量的海面温度的数据集上说明了两种规模的版本，并比较了我们对最先进的空间建模和预测方法的方法。

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