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Maximum Entropy and Bayesian Methods for Image and Spatial Analysis

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Information Theory, Probability and Statistics".

Deadline for manuscript submissions: closed (17 March 2024) | Viewed by 941

Special Issue Editors


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Guest Editor
Bayesian Imaging and Spatial Statistics Group, Institute for Statistics, Ludwig-Maximilians-Universität München, Ludwigstraße 33, 80539 Munich, Germany
Interests: Bayesian statistics; spatial statistics; image analysis and image processing

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Guest Editor Assistant
1. Bayesian Imaging and Spatial Statistics Group, Institute for Statistics, Ludwig-Maximilians-Universität München, Ludwigstraße 33, 80539 Munich, Germany
2. Statistics Department, School of Science, Lorestan University, Khorramabad 68151-44316, Iran
Interests: entropy; maximum entropy method; information theory; Bayesian statistics; copula; optimization problems; inverse problems; mathematical algorithms

Special Issue Information

Dear Colleagues,

The maximum entropy framework (Jaynes, 1957a) is a cornerstone of statistical inference, and it has a privileged position as the only consistent method for combining different data into a single image. It allows us to incorporate extra, prior knowledge about the object being imaged and leads to the selection of a probability density function that is consistent with our knowledge and introduces no unwarranted information. Any probability density function satisfying the constraints that have smaller entropy will contain more information and, hence, less uncertainty.

In a Bayesian view, probabilities are seen as degrees of belief that are modified by information, which is refined as more information becomes available. In the presence of limited information, Bayesian probabilities are often easily assigned where conventional probabilities cannot.

Due to these properties, both maximum entropy and Bayesian approaches have been used massively in image analysis and processing as well as in spatial statistics, i.e., analysis of data observed in geographical space. The combination of Bayesian approaches with the maximum entropy method provides a great inference method.

This Special Issue will accept unpublished original research papers and comprehensive reviews on maximum entropy and Bayesian methods with applications on image data as well as on more general spatial data.

Prof. Dr. Volker J Schmid
Prof. Dr. Zahra Amini Farsani
Guest Editors

Manuscript Submission Information

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Keywords

  • entropy
  • information theory
  • maximum entropy method
  • Bayesian statistics
  • spatial statistics
  • image analysis and image processing

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Published Papers (1 paper)

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Research

40 pages, 10503 KiB  
Article
Variational Bayesian Approximation (VBA): Implementation and Comparison of Different Optimization Algorithms
by Seyedeh Azadeh Fallah Mortezanejad and Ali Mohammad-Djafari
Entropy 2024, 26(8), 707; https://doi.org/10.3390/e26080707 (registering DOI) - 20 Aug 2024
Viewed by 227
Abstract
In any Bayesian computations, the first step is to derive the joint distribution of all the unknown variables given the observed data. Then, we have to do the computations. There are four general methods for performing computations: Joint MAP optimization; Posterior expectation computations [...] Read more.
In any Bayesian computations, the first step is to derive the joint distribution of all the unknown variables given the observed data. Then, we have to do the computations. There are four general methods for performing computations: Joint MAP optimization; Posterior expectation computations that require integration methods; Sampling-based methods, such as MCMC, slice sampling, nested sampling, etc., for generating samples and numerically computing expectations; and finally, Variational Bayesian Approximation (VBA). In this last method, which is the focus of this paper, the objective is to search for an approximation for the joint posterior with a simpler one that allows for analytical computations. The main tool in VBA is to use the Kullback–Leibler Divergence (KLD) as a criterion to obtain that approximation. Even if, theoretically, this can be conducted formally, for practical reasons, we consider the case where the joint distribution is in the exponential family, and so is its approximation. In this case, the KLD becomes a function of the usual parameters or the natural parameters of the exponential family, where the problem becomes parametric optimization. Thus, we compare four optimization algorithms: general alternate functional optimization; parametric gradient-based with the normal and natural parameters; and the natural gradient algorithm. We then study their relative performances on three examples to demonstrate the implementation of each algorithm and their efficiency performance. Full article
(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods for Image and Spatial Analysis)
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