The maximum entropy method of moments and Bayesian probability theory

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8 Scopus citations

Abstract

The problem of density estimation occurs in many disciplines. For example, in MRI it is often necessary to classify the types of tissues in an image. To perform this classification one must first identify the characteristics of the tissues to be classified. These characteristics might be the intensity of a T1 weighted image and in MRI many other types of characteristic weightings (classifiers) may be generated. In a given tissue type there is no single intensity that characterizes the tissue, rather there is a distribution of intensities. Often this distributions can be characterized by a Gaussian, but just as often it is much more complicated. Either way, estimating the distribution of intensities is an inference problem. In the case of a Gaussian distribution, one must estimate the mean and standard deviation. However, in the Non-Gaussian case the shape of the density function itself must be inferred. Three common techniques for estimating density functions are binned histograms [1, 2], kernel density estimation [3, 4], and the maximum entropy method of moments [5, 6]. In the introduction, the maximum entropy method of moments will be reviewed. Some of its problems and conditions under which it fails will be discussed. Then in later sections, the functional form of the maximum entropy method of moments probability distribution will be incorporated into Bayesian probability theory. It will be shown that Bayesian probability theory solves all of the problems with the maximum entropy method of moments. One gets posterior probabilities for the Lagrange multipliers, and, finally, one can put error bars on the resulting estimated density function.

Original languageEnglish
Title of host publicationBayesian Inference and Maximum Entropy Methods in Science and Engineering - 32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering
Pages3-13
Number of pages11
DOIs
StatePublished - 2013
Event32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2012 - Garching, Germany
Duration: Jul 15 2012Jul 20 2012

Publication series

NameAIP Conference Proceedings
Volume1553
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

Conference32nd International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2012
CountryGermany
CityGarching
Period07/15/1207/20/12

Keywords

  • Bayesian probability theory
  • density estimation
  • maximum entropy method of moments

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