错位不规则时间序列的联合推断及其在格陵兰冰芯数据中的应用
Joint Inference of Misaligned Irregular Time Series with Application to Greenland Ice Core Data
摘要：
冰芯提供了对过去数千年气候的深入了解。由于冰的压实，任何单个岩心的原始数据在时间上都是不规则的。多个磁芯具有不同的不规则性;这些系列共同未对准。经过处理后，这些数据作为常规时间序列提供给研究人员：数据产品。通常，这些核被独立地处理。在本文中，我们考虑了一个快速贝叶斯方法的联合处理的多个不规则系列。这被证明是更有效的。此外，我们的方法允许一个现实的建模的影响，多种来源的不确定性。一对冰芯（GISP 2和GRIP）的分析说明了该方法。我们的数据产品，在一个任意的时间网格上的边缘后验分布的形式，是有限的高斯混合。我们还可以从联合后验分布中产生样本路径来研究感兴趣的非线性泛函。更一般地，通过分层高斯过程模型的联合分析的概念可以被广泛地扩展，因为所使用的模型可以在连续时空过程的更大背景下被查看。
英文摘要：
Ice cores provide insight into the past climate over many millennia. Due to ice compaction, the raw data for any single core are irregular in time. Multiple cores have different irregularities; jointly these series are misaligned. After processing, such data are made available to researchers as regular time series: a data product. Typically, these cores are independently processed. In this paper, we consider a fast Bayesian method for the joint processing of multiple irregular series. This is shown to be more efficient. Further, our approach permits a realistic modelling of the impact of the multiple sources of uncertainty. The methodology is illustrated with the analysis of a pair of ice cores (GISP2 and GRIP). Our data products, in the form of marginal posterior distributions on an arbitrary temporal grid, are finite Gaussian mixtures. We can also produce sample paths from the joint posterior distribution to study non-linear functionals of interest. More generally, the concept of joint analysis via hierarchical Gaussian process model can be widely extended as the models used can be viewed within the larger context of continuous space-time processes.
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