通过SCA的高维密度估计：飓风路径模拟的一个例子
High-Dimensional Density Estimation via SCA: An Example in the Modelling of Hurricane Tracks
摘要：
我们提出了非参数技术，从高维数据的不规则依赖结构不能建模的参数多元分布的密度估计的构建和验证。在这种情况下，由于维数灾难，数据的低维表示是至关重要的。我们提出的方法包括三个主要部分：（1）通过降维的数据重新参数化，其中数据被映射到一个空间，在这个空间中，标准技术可以用于密度估计和模拟：（2）逆映射，其中模拟点被映射回高维输入空间;以及（3）验证，其中通过将模拟样本与观测数据进行比较来评估估计的质量。这些方法说明了通过在北大西洋的热带气旋的空间变异性的探索，在这种情况下，每个数据是一个完整的飓风轨迹。最后，我们讨论了扩展的方法来模拟TC变率和气候变量之间的关系。
英文摘要：
We present nonparametric techniques for constructing and verifying density estimates from high-dimensional data whose irregular dependence structure cannot be modelled by parametric multivariate distributions. A low-dimensional representation of the data is critical in such situations because of the curse of dimensionality. Our proposed methodology consists of three main parts: (1) data reparameterization via dimensionality reduction, wherein the data are mapped into a space where standard techniques can be used for density estimation and simulation; (2) inverse mapping, in which simulated points are mapped back to the high-dimensional input space; and (3) verification, in which the quality of the estimate is assessed by comparing simulated samples with the observed data. These approaches are illustrated via an exploration of the spatial variability of tropical cyclones in the North Atlantic; each datum in this case is an entire hurricane trajectory. We conclude the paper with a discussion of extending the methods to model the relationship between TC variability and climatic variables.
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