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...
This is a preview of subscription content, access via your institution.
Abbreviations
- MEM:
-
maximum entropy method
- MaxEnt:
-
maximum entropy
- BME:
-
Bayesian Maximum entropy
Bibliography
Burg JP (1972) The relationship between maximum entropy spectra and maximum likelihood spectra. Geophysics 37(2):375–376
Christakos G (1990) A Bayesian/maximum-entropy view to the spatial estimation problem. Math Geol 22(7):763–777
Christakos G (2000) Modern spatiotemporal geostatistics, International Association for Mathematical Geology Studies in mathematical geology, vol 6. Oxford University Press, Oxford
Hristopulos DT (2020) Random fields for spatial data modeling: a primer for scientists and engineers. Springer Netherlands, Dordrecht
Jaynes ET (1957a) Information theory and statistical mechanics. I. Phys Rev 106(4):620–630
Jaynes ET (1957b) Information theory and statistical mechanics. II. Phys Rev 108(2):171–190
Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27(3):379–423
Skilling J (2013) Maximum entropy and Bayesian methods: Cambridge, England, 1988, vol 36. Springer Science & Business Media, Cham
Skilling J, Bryan R (1984) Maximum entropy image reconstruction-general algorithm. Mon Not R Astron Soc 211:111–124
Ulrych TJ, Bishop TN (1975) Maximum entropy spectral analysis and autoregressive decomposition. Rev Geophys 13(1):183–200
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this entry
Cite this entry
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-26050-7_196-1
Received:
Accepted:
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-26050-7
Online ISBN: 978-3-030-26050-7
eBook Packages: Springer Reference Earth & Environm. ScienceReference Module Physical and Materials Science