III. Tsallis Theory, the Maximum Entropy Principle, and Evolution Equations

2007 ◽  
pp. 157-191 ◽  
Author(s):  
A.R. Plastino
Keyword(s):  
Maximum Entropy ◽  
Evolution Equations ◽  
Maximum Entropy Principle ◽  
Entropy Principle

Maximum entropy principle and classical evolution equations with source terms

2007 ◽  
Vol 374 (2) ◽  
pp. 573-584 ◽  
Author(s):  
J-H. Schönfeldt ◽  
N. Jimenez ◽  
A.R. Plastino ◽  
A. Plastino ◽  
M. Casas
Keyword(s):  
Maximum Entropy ◽  
Evolution Equations ◽  
Maximum Entropy Principle ◽  
Source Terms ◽  
Entropy Principle ◽  
Classical Evolution

An entropy concentration theorem: applications in artificial intelligence and descriptive statistics

1990 ◽  
Vol 27 (2) ◽  
pp. 303-313 ◽  
Author(s):  
Claudine Robert
Keyword(s):  
Artificial Intelligence ◽  
Maximum Entropy ◽  
Large Deviation ◽  
Maximum Entropy Principle ◽  
Statistical Modelling ◽  
Linear Constraints ◽  
Descriptive Statistics ◽  
Entropy Principle ◽  
Maximum Entropy Distribution ◽  
Mathematical Justification

The maximum entropy principle is used to model uncertainty by a maximum entropy distribution, subject to some appropriate linear constraints. We give an entropy concentration theorem (whose demonstration is based on large deviation techniques) which is a mathematical justification of this statistical modelling principle. Then we indicate how it can be used in artificial intelligence, and how relevant prior knowledge is provided by some classical descriptive statistical methods. It appears furthermore that the maximum entropy principle yields to a natural binding between descriptive methods and some statistical structures.

SINE ENTROPY FOR UNCERTAIN VARIABLES

2013 ◽  
Vol 21 (05) ◽  
pp. 743-753 ◽  
Author(s):  
KAI YAO ◽  
JINWU GAO ◽  
WEI DAI
Keyword(s):  
Maximum Entropy ◽  
Uncertainty Theory ◽  
Maximum Entropy Principle ◽  
Expected Value ◽  
Uncertain Variables ◽  
Entropy Principle

Entropy is a measure of the uncertainty associated with a variable whose value cannot be exactly predicated. In uncertainty theory, it has been quantified so far by logarithmic entropy. However, logarithmic entropy sometimes fails to measure the uncertainty. This paper will propose another type of entropy named sine entropy as a supplement, and explore its properties. After that, the maximum entropy principle will be introduced, and the arc-cosine distributed variables will be proved to have the maximum sine entropy with given expected value and variance.

scholarly journals Maximum-entropy principle: ecological organization and evolution

2009 ◽  
Vol 36 (2) ◽  
pp. 175-183 ◽  
Author(s):  
C. G. Chakrabarti ◽  
Koyel Ghosh
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Principle ◽  
Entropy Principle
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