Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions—such as random rectangles or histograms—each describing a portion of the larger dataset. Recent work has developed likelihood-based methods that permit fitting models for the underlying data while only observing the distributional summaries. However, while powerful, when working with random histograms this approach rapidly becomes computationally intractable as the dimension of the underlying data increases. We introduce a composite-likelihood variation of this likelihood-based approach for the analysis of random histograms in K dimensions, through the construction of lower-dimensional marginal histograms. The performance of this approach is examined through simulated and real data analysis of max-stable models for spatial extremes using millions of observed datapoints in more than \(K=100\) dimensions. Large computational savings are available compared to existing model fitting approaches.

中文翻译：

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直方图值随机变量的复合似然方法

已经提出符号数据分析作为一种技术，用于将大型和复杂的数据集汇总为更小且易于处理的数量分布（例如随机矩形或直方图），每个分布都描述了较大数据集的一部分。最近的工作已经开发了基于似然性的方法，该方法允许在仅观察分布汇总的同时对基础数据进行拟合模型。但是，尽管功能强大，但是当处理随机直方图时，随着基础数据维数的增加，此方法在计算上会变得很棘手。我们介绍了这种基于可能性的方法的复合似然变化，用于分析K中的随机直方图通过构建低维的边际直方图来构建维度。通过对空间极限的最大稳定模型的模拟和真实数据分析，使用了超过（K = 100 \）个维度的数百万个观测数据点，对该方法的性能进行了检验。与现有的模型拟合方法相比，可节省大量计算量。