In this paper, we introduce a model for multivariate, spatio-temporal functional data. Specifically, this work proposes a mixture model that is used to perform spatio-temporal prediction (cokriging) when both the response and the additional covariates are functional data. The estimation of such models in the context of expansive data poses many methodological and computational challenges. We propose a new Monte Carlo Expectation Maximization algorithm based on importance sampling to estimate model parameters. We validate our methodology using simulation studies and provide a comparison to previously proposed functional clustering methodologies. To tackle computational challenges, we describe a variety of advances that enable application on large spatio-temporal datasets. The methodology is applied on Argo oceanographic data in the Southern Ocean to predict oxygen concentration, which is critical to ocean biodiversity and reflects fundamental aspects of the carbon cycle. Our model and implementation comprehensively provide oxygen predictions and their estimated uncertainty as well as recover established oceanographic fronts.
翻译:在本文中,我们引入了一个多变量、时空功能数据模型。具体地说,这项工作提出了一个混合模型,用于在反应和额外共变都是功能性数据时进行时空预测(cokriging),在扩展数据背景下对此类模型进行估算,在方法和计算方面提出了许多挑战。我们根据重要抽样,提出了一个新的蒙特卡洛期望最大化算法,以估计模型参数。我们利用模拟研究验证了我们的方法,并提供了与先前提议的功能组群方法的比较。为了应对计算挑战,我们描述了能够应用大型时空云层数据集的各种进展。该方法适用于南大洋的阿尔戈海洋学数据,以预测氧浓度,这对海洋生物多样性至关重要,反映了碳循环的基本方面。我们的模型和执行全面提供了氧预测及其估计不确定性,并恢复了既定的海洋学前沿。