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题名: Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample
作者: Sui, N ;  Li, M ;  He, P
刊名: MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
出版日期: 2014
卷号: 445, 期号:4, 页码:4211-4217
关键词: SELF-GRAVITATING SYSTEMS ;  MECHANICS ;  DISTRIBUTIONS ;  CHOICE
学科分类: Physics
DOI: 10.1093/mnras/stu2040
通讯作者: Sui, N (reprint author), Jilin Univ, Coll Phys, Changchun 130012, Peoples R China.
部门归属: [Sui, Ning ;  He, Ping] Jilin Univ, Coll Phys, Changchun 130012, Peoples R China ;  [Li, Min] Chinese Acad Sci, Changchun Artificial Satellite Observ, Changchun 130117, Peoples R China ;  [He, Ping] Peking Univ, Ctr High Energy Phys, Beijing 100871, Peoples R China ;  [He, Ping] Chinese Acad Sci, Inst Theoret Phys, State Key Lab Theoret Phys, Beijing 100190, Peoples R China
英文摘要: In this work, we investigate the statistical computation of the Boltzmann entropy of statistical samples. For this purpose, we use both histogram and kernel function to estimate the probability density function of statistical samples. We find that, due to coarse-graining, the entropy is a monotonic increasing function of the bin width for histogram or bandwidth for kernel estimation, which seems to be difficult to select an optimal bin width/bandwidth for computing the entropy. Fortunately, we notice that there exists a minimum of the first derivative of entropy for both histogram and kernel estimation, and this minimum point of the first derivative asymptotically points to the optimal bin width or bandwidth. We have verified these findings by large amounts of numerical experiments. Hence, we suggest that the minimum of the first derivative of entropy be used as a selector for the optimal bin width or bandwidth of density estimation. Moreover, the optimal bandwidth selected by the minimum of the first derivative of entropy is purely data-based, independent of the unknown underlying probability density distribution, which is obviously superior to the existing estimators. Our results are not restricted to one-dimensional, but can also be extended to multivariate cases. It should be emphasized, however, that we do not provide a robust mathematical proof of these findings, and we leave these issues with those who are interested in them.
资助者: National Basic Research Program of China [2010CB832805]; National Science Foundation of China [11273013]; State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China [Y4KF121CJ1]
收录类别: SCI
原文出处: 查看原文
语种: 英语
WOS记录号: WOS:000346963300068
Citation statistics: 
内容类型: 期刊论文
URI标识: http://ir.itp.ac.cn/handle/311006/15534
Appears in Collections:理论物理所2014年知识产出 _期刊论文

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Recommended Citation:
Sui, N,Li, M,He, P. Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample[J]. MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,2014,445(4):4211-4217.
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