scholarly journals Construction of probability distributions in high dimension using the maximum entropy principle: Applications to stochastic processes, random fields and random matrices

2008 ◽  
Vol 76 (10) ◽  
pp. 1583-1611 ◽  
Author(s):  
Christian Soize
Keyword(s):  
Stochastic Processes ◽  
Maximum Entropy ◽  
Random Matrices ◽  
High Dimension ◽  
Random Fields ◽  
Probability Distributions ◽  
Maximum Entropy Principle ◽  
Entropy Principle

scholarly journals Inferences from a network to a subnetwork and vice versa under an assumption of symmetry

2015 ◽  
Author(s):  
PierGianLuca Porta Mana ◽  
Emiliano Torre ◽  
Vahid Rostami
Keyword(s):  
Probability Theory ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Maximum Entropy Principle ◽  
Entropy Principle ◽  
Mathematical Relations

This note summarizes some mathematical relations between the probability distributions for the states of a network of binary units and a subnetwork thereof, under an assumption of symmetry. These relations are standard results of probability theory, but seem to be rarely used in neuroscience. Some of their consequences for inferences between network and subnetwork, especially in connection with the maximum-entropy principle, are briefly discussed. The meanings and applicability of the assumption of symmetry are also discussed.

Use in Probabilistic Design of the Maximum Entrophy Distribution Based on Ranked Data

1980 ◽  
Vol 102 (3) ◽  
pp. 460-468
Author(s):  
J. N. Siddall ◽  
Ali Badawy
Keyword(s):  
Probability Distribution ◽  
Maximum Entropy ◽  
Probability Distributions ◽  
Maximum Entropy Principle ◽  
Random Variable ◽  
Probabilistic Design ◽  
Entropy Principle ◽  
Almost All ◽  
New Distribution

A new algorithm using the maximum entropy principle is introduced to estimate the probability distribution of a random variable, using directly a ranked sample. It is demonstrated that almost all of the analytical probability distributions can be approximated by the new algorithm. A comparison is made between existing methods and the new algorithm; and examples are given of fitting the new distribution to an actual ranked sample.

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