Unification of some deterministic and probabilistic methods for the solution of linear inverse problems via the principle of maximum entropy on the mean

In this study, the distribution of sediment concentration and the mean sediment concentration in debris flow were investigated using deterministic and probabilistic approaches. Tsallis entropy and Shannon entropy have recently been employed to estimate these parameters. However, other entropy theories, such as the general index entropy and Renyi entropy theories, which are generalizations of the Shannon entropy, have not been used to derive the sediment concentration in debris flow. Furthermore, no comprehensive and rigorous analysis has been conducted to compare the goodness of fit of existing conventional deterministic methods and different entropy-based methods using experimental data collected from the literature. Therefore, this study derived the analytical expressions for the distribution of sediment concentration and the mean sediment concentration in debris flow based on the general index entropy and Renyi entropy theories together with the principle of maximum entropy and tested the validity of existing conventional deterministic methods as well as four different entropy-based expressions for the limited collected observational data. This study shows the potential of using the Tsallis entropy theory together with the principle of maximum entropy to predict sediment concentration in debris flow over an erodible channel bed.

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O Princípio da Máxima Entropia e a Moderna Teoria das Carteiras

Brazilian Review of Finance ◽

10.12660/rbfin.v1n2.2003.1131 ◽

2003 ◽

Vol 1 (2) ◽

pp. 271

Author(s):

Ailton Cassetari

Keyword(s):

At Risk ◽

Maximum Entropy ◽

Value At Risk ◽

Capital Allocation ◽

Systematic Comparison ◽

Principle Of Maximum Entropy ◽

The Mean ◽

Mean Variance ◽

Principle Of Maximum ◽

Risk Concept

In this work, a capital allocation methodology base don the Principle of Maximum Entropy was developed. The Shannons entropy is used as a measure, concerning the Modern Portfolio Theory, are also discuted. Particularly, the methodology is tested making a systematic comparison to: 1) the mean-variance (Markovitz) approach and 2) the mean VaR approach (capital allocations based on the Value at Risk concept). In principle, such confrontations show the plausibility and effectiveness of the developed method.

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To Be or to Have Been Lucky, That Is the Question

Philosophies ◽

10.3390/philosophies6030057 ◽

2021 ◽

Vol 6 (3) ◽

pp. 57

Author(s):

Antony Lesage ◽

Jean-Marc Victor

Keyword(s):

High Risk ◽

Maximum Entropy ◽

Chronic Diseases ◽

Statistical Test ◽

Low Risk ◽

Principle Of Maximum Entropy ◽

Ex Ante ◽

Social Opportunities ◽

Global Population ◽

Principle Of Maximum

Is it possible to measure the dispersion of ex ante chances (i.e., chances “before the event”) among people, be it gambling, health, or social opportunities? We explore this question and provide some tools, including a statistical test, to evidence the actual dispersion of ex ante chances in various areas, with a focus on chronic diseases. Using the principle of maximum entropy, we derive the distribution of the risk of becoming ill in the global population as well as in the population of affected people. We find that affected people are either at very low risk, like the overwhelming majority of the population, but still were unlucky to become ill, or are at extremely high risk and were bound to become ill.

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