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More on Estimation

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Random Fields for Spatial Data Modeling

Part of the book series: Advances in Geographic Information Science ((AGIS))

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Abstract

This chapter discusses estimation methods that are less established and not as commonly used as those presented in the preceding chapter. For example, the method of normalized correlations is relatively new, and its statistical properties have not been fully explored. The method of maximum entropy was used by Edwin Thompson Jaynes to derive statistical mechanics based on information theory [406, 407]. Following the work of Jaynes, maximum entropy has found several applications in physics [674, 753], image processing [315, 754], and machine learning [521, 561].

In desperation I asked Fermi whether he was not impressed by the agreement between our calculated numbers and his measured numbers. He replied, “How many arbitrary parameters did you use for your calculations?” I thought for a moment about our cut-off procedures and said, “Four.” He said, “I remember my friend Johnny von Neumann used to say, with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.”

Freeman Dyson

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Notes

  1. 1.

    To review constrained optimization with Lagrange multipliers consider [673, Chap. 16.5] and [67].

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Hristopulos, D.T. (2020). More on Estimation. In: Random Fields for Spatial Data Modeling. Advances in Geographic Information Science. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1918-4_13

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