ITP OpenIR  > 理论物理所科研产出  > SCI论文
Sui, N; Li, M; He, P; Sui, N (reprint author), Jilin Univ, Coll Phys, Changchun 130012, Peoples R China.
Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample
Source PublicationMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
Language英语
KeywordSelf-gravitating Systems Mechanics Distributions Choice
AbstractIn 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.
2014
ISSN0035-8711
Volume445Issue:4Pages:4211-4217
Subject AreaPhysics
DOI10.1093/mnras/stu2040
Indexed BySCI
Funding OrganizationNational 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] ; 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] ; 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] ; 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]
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/15534
Collection理论物理所科研产出_SCI论文
Corresponding AuthorSui, N (reprint author), Jilin Univ, Coll Phys, Changchun 130012, Peoples R China.
Recommended Citation
GB/T 7714
Sui, N,Li, M,He, P,et al. 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.
APA Sui, N,Li, M,He, P,&Sui, N .(2014).Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample.MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,445(4),4211-4217.
MLA Sui, N,et al."Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample".MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 445.4(2014):4211-4217.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Sui, N]'s Articles
[Li, M]'s Articles
[He, P]'s Articles
Baidu academic
Similar articles in Baidu academic
[Sui, N]'s Articles
[Li, M]'s Articles
[He, P]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Sui, N]'s Articles
[Li, M]'s Articles
[He, P]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.