The essential histogram
针对直方图分箱数选择难题，构造分布函数置信集，从中选出箱数最少且能最优完成概率估计和特征检测的直方图，即本质直方图，并提供快速算法。
Summary The histogram is widely used as a simple, exploratory way of displaying data, but it is usually not clear how to choose the number and size of the bins. We construct a confidence set of distribution functions that optimally deal with the two main tasks of the histogram: estimating probabilities and detecting features such as increases and modes in the distribution. We define the essential histogram as the histogram in the confidence set with the fewest bins. Thus the essential histogram is the simplest visualization of the data that optimally achieves the main tasks of the histogram. The only assumption we make is that the data are independent and identically distributed. We provide a fast algorithm for computing the essential histogram and illustrate our method with examples.