ITP OpenIR  > 理论物理所2014年知识产出
Statistical computation of Boltzmann entropy and estimation of the optimal probability density function from statistical sample
Sui, N; Li, M; He, P; Sui, N (reprint author), Jilin Univ, Coll Phys, Changchun 130012, Peoples R China.
2014
发表期刊MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
ISSN0035-8711
卷号445期号:4页码:4211-4217
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.
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
关键词Self-gravitating Systems Mechanics Distributions Choice
学科领域Physics
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] ; 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]
DOI10.1093/mnras/stu2040
URL查看原文
收录类别SCI
语种英语
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] ; 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]
WOS记录号WOS:000346963300068
引用统计
被引频次:2[WOS]   [WOS记录]     [WOS相关记录]
文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/15534
专题理论物理所2014年知识产出
通讯作者Sui, N (reprint author), Jilin Univ, Coll Phys, Changchun 130012, Peoples R China.
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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.
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