期刊
DIGITAL SIGNAL PROCESSING
卷 95, 期 -, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.dsp.2019.102581
关键词
Binning data; Histogram; Probability density; Density models; Small sample size; Sufficient data
资金
- NASA Earth-Sun Systems Technology Office Applied Information Systems Technology Program
- NASA Applied Information Systems Research Program [NASA AISRP NNH05ZDA001N, NASA ESTC NNX07AD97A, NNX07AN04G]
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. (C) 2019 Elsevier Inc. All rights reserved.
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