Knowledge Management System of Institute of Theoretical Physics, CAS
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 Publication | MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY |
Language | 英语 |
Keyword | Self-gravitating Systems Mechanics Distributions Choice |
Abstract | 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. |
2014 | |
ISSN | 0035-8711 |
Volume | 445Issue:4Pages:4211-4217 |
Subject Area | Physics |
DOI | 10.1093/mnras/stu2040 |
Indexed By | SCI |
Funding Organization | 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] |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.itp.ac.cn/handle/311006/15534 |
Collection | 理论物理所科研产出_SCI论文 |
Corresponding Author | Sui, 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. |
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