基于数据的直方图最优分箱
Optimal Data-Based Binning for Histograms
摘要：
直方图是一种方便的非参数密度估计器，一直被广泛使用。从基于直方图的概率密度模型估计的汇总数量取决于箱数的选择。我们介绍了一个简单的基于数据的方法，确定在一个统一的箱宽度直方图的最佳数量的箱。通过分配一个多项式似然和一个非信息先验，我们推导出给定数据的分段常数密度模型中箱数的后验概率。此外，我们估计的平均值和标准偏差的结果箱高度，检查小样本量和数字化数据的影响，并展示了应用程序的多维直方图。
英文摘要：
Histograms are convenient non-parametric density estimators, which continue to be used ubiquitously. Summary quantities estimated from histogram-based probability density models depend on the choice of the number of bins. We introduce a straightforward data-based method of determining the optimal number of bins in a uniform bin-width histogram. By assigning a multinomial likelihood and a non-informative prior, we derive the posterior probability for the number of bins in a piecewise-constant density model given the data. In addition, we estimate the mean and standard deviations of the resulting bin heights, examine the effects of small sample sizes and digitized data, and demonstrate the application to multi-dimensional histograms.
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