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Maximum Entropy Method

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Encyclopedia of Mathematical Geosciences

Definition

The principle of maximum entropy states that the most suitable probability model for a given system maximizes the Shannon entropy subject to the constraints imposed by the data and – if available – other prior knowledge of the system. The maximum entropy distribution is the most general probability distribution function conditionally on the constraints. In the geosciences, the principle of maximum entropy is mainly used in two ways: (1) in the maximum entropy method (MEM) for the parametric estimation of the power spectrum and (2) for constructing joint probability models suitable for spatial and spatiotemporal datasets.

Overview

The concept of entropy was introduced in thermodynamics by the German physicist Rudolf Clausius in the nineteenth century. Clausius used entropy to measure the thermal energy of a machine per unit temperature which cannot be used to generate useful work. The Austrian physicist Ludwig Boltzmann used entropy in statistical mechanics to quantify the ran...

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Abbreviations

MEM:

maximum entropy method

MaxEnt:

maximum entropy

BME:

Bayesian Maximum entropy

Bibliography

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Correspondence to Dionissios T. Hristopulos .

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Hristopulos, D.T., Varouchakis, E.A. (2021). Maximum Entropy Method. In: Daya Sagar, B., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-26050-7_196-1

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  • DOI: https://doi.org/10.1007/978-3-030-26050-7_196-1

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  • Print ISBN: 978-3-030-26050-7

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