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Special Issue "Maximum Entropy and Bayesian Methods"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: 31 August 2017

Special Issue Editor

Guest Editor
Dr. Brendon J. Brewer

Department of Statistics, The University of Auckland, Private Bag 92019, Auckland 1142, New Zealand
Website | E-Mail
Phone: +64275001336
Interests: bayesian inference, markov chain monte carlo, nested sampling, MaxEnt

Special Issue Information

Dear Colleagues,

Whereas Bayesian inference has now achieved mainstream acceptance and is widely used throughout the sciences, associated ideas such as the principle of maximum entropy (implicit in the work of Gibbs, and developed further by Ed Jaynes and others) have not. There are strong arguments that the principle (and variations, such as maximum relative entropy) is of fundamental importance, but the literature also contains many misguided attempts at applying it, leading to much confusion.

This Special Issue will focus on Bayesian inference and MaxEnt. Some open questions that spring to mind are: Which proposed ways of using entropy (and its maximisation) in inference are legitimate, which are not, and why? Where can we obtain constraints on probability assignments, the input needed by the MaxEnt procedure?

More generally, papers exploring any interesting connections between probabilistic inference and information theory will be considered. Papers presenting high quality applications, or discussing computational methods in these areas, are also welcome.

Dr. Brendon J. Brewer
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1500 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Bayesian inference;
  • Uncertainty;
  • Maximum Entropy;
  • Maximum Relative Entropy;
  • Prior Distributions;
  • Principle of Indifference;
  • Symmetry;
  • Relevance

Published Papers (3 papers)

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Research

Open AccessArticle Optimal Detection under the Restricted Bayesian Criterion
Entropy 2017, 19(7), 370; doi:10.3390/e19070370
Received: 8 May 2017 / Revised: 11 July 2017 / Accepted: 18 July 2017 / Published: 19 July 2017
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Abstract
This paper aims to find a suitable decision rule for a binary composite hypothesis-testing problem with a partial or coarse prior distribution. To alleviate the negative impact of the information uncertainty, a constraint is considered that the maximum conditional risk cannot be greater
[...] Read more.
This paper aims to find a suitable decision rule for a binary composite hypothesis-testing problem with a partial or coarse prior distribution. To alleviate the negative impact of the information uncertainty, a constraint is considered that the maximum conditional risk cannot be greater than a predefined value. Therefore, the objective of this paper becomes to find the optimal decision rule to minimize the Bayes risk under the constraint. By applying the Lagrange duality, the constrained optimization problem is transformed to an unconstrained optimization problem. In doing so, the restricted Bayesian decision rule is obtained as a classical Bayesian decision rule corresponding to a modified prior distribution. Based on this transformation, the optimal restricted Bayesian decision rule is analyzed and the corresponding algorithm is developed. Furthermore, the relation between the Bayes risk and the predefined value of the constraint is also discussed. The Bayes risk obtained via the restricted Bayesian decision rule is a strictly decreasing and convex function of the constraint on the maximum conditional risk. Finally, the numerical results including a detection example are presented and agree with the theoretical results. Full article
(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods)
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Open AccessArticle A Bayesian Optimal Design for Sequential Accelerated Degradation Testing
Entropy 2017, 19(7), 325; doi:10.3390/e19070325
Received: 16 May 2017 / Revised: 21 June 2017 / Accepted: 27 June 2017 / Published: 1 July 2017
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Abstract
When optimizing an accelerated degradation testing (ADT) plan, the initial values of unknown model parameters must be pre-specified. However, it is usually difficult to obtain the exact values, since many uncertainties are embedded in these parameters. Bayesian ADT optimal design was presented to
[...] Read more.
When optimizing an accelerated degradation testing (ADT) plan, the initial values of unknown model parameters must be pre-specified. However, it is usually difficult to obtain the exact values, since many uncertainties are embedded in these parameters. Bayesian ADT optimal design was presented to address this problem by using prior distributions to capture these uncertainties. Nevertheless, when the difference between a prior distribution and actual situation is large, the existing Bayesian optimal design might cause some over-testing or under-testing issues. For example, the implemented ADT following the optimal ADT plan consumes too much testing resources or few accelerated degradation data are obtained during the ADT. To overcome these obstacles, a Bayesian sequential step-down-stress ADT design is proposed in this article. During the sequential ADT, the test under the highest stress level is firstly conducted based on the initial prior information to quickly generate degradation data. Then, the data collected under higher stress levels are employed to construct the prior distributions for the test design under lower stress levels by using the Bayesian inference. In the process of optimization, the inverse Gaussian (IG) process is assumed to describe the degradation paths, and the Bayesian D-optimality is selected as the optimal objective. A case study on an electrical connector’s ADT plan is provided to illustrate the application of the proposed Bayesian sequential ADT design method. Compared with the results from a typical static Bayesian ADT plan, the proposed design could guarantee more stable and precise estimations of different reliability measures. Full article
(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods)
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Open AccessArticle Bayesian Hierarchical Scale Mixtures of Log-Normal Models for Inference in Reliability with Stochastic Constraint
Entropy 2017, 19(6), 274; doi:10.3390/e19060274
Received: 2 May 2017 / Revised: 3 June 2017 / Accepted: 9 June 2017 / Published: 13 June 2017
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Abstract
This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT) models with stochastic (or uncertain) constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT) models (such as log-normal, log-Cauchy,
[...] Read more.
This paper develops Bayesian inference in reliability of a class of scale mixtures of log-normal failure time (SMLNFT) models with stochastic (or uncertain) constraint in their reliability measures. The class is comprehensive and includes existing failure time (FT) models (such as log-normal, log-Cauchy, and log-logistic FT models) as well as new models that are robust in terms of heavy-tailed FT observations. Since classical frequency approaches to reliability analysis based on the SMLNFT model with stochastic constraint are intractable, the Bayesian method is pursued utilizing a Markov chain Monte Carlo (MCMC) sampling based approach. This paper introduces a two-stage maximum entropy (MaxEnt) prior, which elicits a priori uncertain constraint and develops Bayesian hierarchical SMLNFT model by using the prior. The paper also proposes an MCMC method for Bayesian inference in the SMLNFT model reliability and calls attention to properties of the MaxEnt prior that are useful for method development. Finally, two data sets are used to illustrate how the proposed methodology works. Full article
(This article belongs to the Special Issue Maximum Entropy and Bayesian Methods)
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