The principle of the maximum entropy method

Makoto Sakata; Masaki Takata

The principle of the maximum entropy method

Research output: Contribution to journal › Article › peer-review

Abstract

The theoretical background of the maximum entropy method (MEM) when it is applied to restore the electron or nuclear densities from diffraction data is described. In MEM, the concept of "entropy" is introduced to deal with any incompleteness in an observation in a proper way. An incompleteness causes some ambiguities in the results to some extent. The essence of the method is to find a solution which necessarily agrees with the observation, leaving the measure of ambiguities (entropy) maximum. A few results for simple structures with typical types of chemical bonding are also presented.

Original language	English
Pages (from-to)	327-333
Number of pages	7
Journal	High Pressure Research
Volume	14
Issue number	4-5
Publication status	Published - 1996
Externally published	Yes

Keywords

Electron density distribution
Maximum entropy method
Powder diffraction
Silicon

ASJC Scopus subject areas

Condensed Matter Physics

Cite this

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title = "The principle of the maximum entropy method",

abstract = "The theoretical background of the maximum entropy method (MEM) when it is applied to restore the electron or nuclear densities from diffraction data is described. In MEM, the concept of {"}entropy{"} is introduced to deal with any incompleteness in an observation in a proper way. An incompleteness causes some ambiguities in the results to some extent. The essence of the method is to find a solution which necessarily agrees with the observation, leaving the measure of ambiguities (entropy) maximum. A few results for simple structures with typical types of chemical bonding are also presented.",

keywords = "Electron density distribution, Maximum entropy method, Powder diffraction, Silicon",

author = "Makoto Sakata and Masaki Takata",

note = "Funding Information: The authors thank Dr. C. J. Howard for supplying the powder neutron-diffraction data of Si. This work was supported by Grant-in-Aid for Research from the Ministry of Education, Science and Culture. This work was also partly supported by Photon Factory.",

year = "1996",

language = "English",

volume = "14",

pages = "327--333",

journal = "High Pressure Research",

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T1 - The principle of the maximum entropy method

AU - Sakata, Makoto

AU - Takata, Masaki

N1 - Funding Information: The authors thank Dr. C. J. Howard for supplying the powder neutron-diffraction data of Si. This work was supported by Grant-in-Aid for Research from the Ministry of Education, Science and Culture. This work was also partly supported by Photon Factory.

PY - 1996

Y1 - 1996

N2 - The theoretical background of the maximum entropy method (MEM) when it is applied to restore the electron or nuclear densities from diffraction data is described. In MEM, the concept of "entropy" is introduced to deal with any incompleteness in an observation in a proper way. An incompleteness causes some ambiguities in the results to some extent. The essence of the method is to find a solution which necessarily agrees with the observation, leaving the measure of ambiguities (entropy) maximum. A few results for simple structures with typical types of chemical bonding are also presented.

AB - The theoretical background of the maximum entropy method (MEM) when it is applied to restore the electron or nuclear densities from diffraction data is described. In MEM, the concept of "entropy" is introduced to deal with any incompleteness in an observation in a proper way. An incompleteness causes some ambiguities in the results to some extent. The essence of the method is to find a solution which necessarily agrees with the observation, leaving the measure of ambiguities (entropy) maximum. A few results for simple structures with typical types of chemical bonding are also presented.

KW - Electron density distribution

KW - Maximum entropy method

KW - Powder diffraction

KW - Silicon

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JO - High Pressure Research

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The principle of the maximum entropy method

Abstract

Keywords

ASJC Scopus subject areas

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