直方图值随机变量的复合似然方法
Composite likelihood methods for histogram-valued random variables
摘要：
符号数据分析已经被提出作为一种技术，用于将大型和复杂的数据集总结为更小和易于处理的分布数量-例如随机矩形或直方图-每个描述较大数据集的一部分。最近的工作已经开发出基于似然的方法，允许拟合模型的基础数据，而只观察分布摘要。然而，虽然功能强大，但当处理随机直方图时，随着底层数据的维度增加，这种方法在计算上迅速变得难以处理。我们引入了一个复合似然变化的可能性为基础的方法分析随机直方图在$K$维度，通过建设低维边缘直方图。这种方法的性能进行检查，通过模拟和真实的数据分析的最大稳定模型的空间极值，使用数百万个观测数据点在多个$K=100$尺寸。与现有的模型拟合方法相比，可以节省大量的计算。
英文摘要：
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.
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