Special Issue "Applications of Fisher Information in Sciences"

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

Deadline for manuscript submissions: closed (30 April 2016).

Special Issue Editor

Dr. Takuya Yamano

Guest Editor
Department of Mathematics and Physics, Faculty of Science, Kanagawa University, 2946,6-233 Tsuchiya, Hiratsuka, Kanagawa 259-1293, Japan
Interests: Fisher information; nonextensivity; information theory; nonlinear Fokker-Planck equations; nonlinear Schrödinger equations; complexity measure; irreversibility; tumor growth; temperature-dependent energy levels in statistical physics
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Special Issue Information

Dear Colleagues,

Fisher information was originally put forth in statistical estimation theory and it has been an important tool to analyze systems. Although it has not received enough attention from researchers in other fields, this unappreciated situation seem to be changing gradually. Indeed, statistical physics and thermodynamics have a deep relation to this notion. In addition, astronomy, as well as biosciences, reap most of the benefits through big data analysis via Fisher information.

In this Special Issue, we would like to focus on the various aspects of Fisher information and its applications in sciences. Papers that broaden the horizon are welcome.

Dr. Takuya Yamano
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 1600 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

  • fisher information
  • relative Fisher information
  • quantum Fisher information
  • extreme physical information principle
  • statistical estimation theory
  • Bruijn’s identity
  • Cramer–Rao bound
  • gradient flow
  • logarithmic Sobolev inequality
  • phase space gradient
  • information geometry
  • data analysis

Published Papers (4 papers)

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Open AccessArticle
Structures in Sound: Analysis of Classical Music Using the Information Length
Entropy 2016, 18(7), 258; https://doi.org/10.3390/e18070258 - 13 Jul 2016
Cited by 16
Abstract
We show that music is represented by fluctuations away from the minimum path through statistical space. Our key idea is to envision music as the evolution of a non-equilibrium system and to construct probability distribution functions (PDFs) from musical instrument digital interface (MIDI) [...] Read more.
We show that music is represented by fluctuations away from the minimum path through statistical space. Our key idea is to envision music as the evolution of a non-equilibrium system and to construct probability distribution functions (PDFs) from musical instrument digital interface (MIDI) files of classical compositions. Classical music is then viewed through the lens of generalized position and velocity, based on the Fisher metric. Through these statistical tools we discuss a way to quantitatively discriminate between music and noise. Full article
(This article belongs to the Special Issue Applications of Fisher Information in Sciences)
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Open AccessArticle
The Fisher Thermodynamics of Quasi-Probabilities
Entropy 2015, 17(12), 7848-7858; https://doi.org/10.3390/e17127853 - 27 Nov 2015
Cited by 1
Abstract
With reference to Lee’s treatment of quasi-probabilities, it is seen that the three phase space quasi-probabilities, known as the P-, Husimi and Wigner ones, plus other intermediate ones, generate a common, single Fisher thermodynamics, along the lines developed by Frieden et al. We [...] Read more.
With reference to Lee’s treatment of quasi-probabilities, it is seen that the three phase space quasi-probabilities, known as the P-, Husimi and Wigner ones, plus other intermediate ones, generate a common, single Fisher thermodynamics, along the lines developed by Frieden et al. We explore some facets of such thermodynamics and encounter complementarity between two different kinds of Fisher information. Full article
(This article belongs to the Special Issue Applications of Fisher Information in Sciences)
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Review

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Open AccessReview
Generalisations of Fisher Matrices
Entropy 2016, 18(6), 236; https://doi.org/10.3390/e18060236 - 22 Jun 2016
Cited by 3
Abstract
Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters—both their errors and covariances. In this short review, I outline a number of extensions to the simple [...] Read more.
Fisher matrices play an important role in experimental design and in data analysis. Their primary role is to make predictions for the inference of model parameters—both their errors and covariances. In this short review, I outline a number of extensions to the simple Fisher matrix formalism, covering a number of recent developments in the field. These are: (a) situations where the data (in the form of ( x , y ) pairs) have errors in both x and y; (b) modifications to parameter inference in the presence of systematic errors, or through fixing the values of some model parameters; (c) Derivative Approximation for LIkelihoods (DALI) - higher-order expansions of the likelihood surface, going beyond the Gaussian shape approximation; (d) extensions of the Fisher-like formalism, to treat model selection problems with Bayesian evidence. Full article
(This article belongs to the Special Issue Applications of Fisher Information in Sciences)
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Open AccessReview
Estimating a Repeatable Statistical Law by Requiring Its Stability During Observation
Entropy 2015, 17(11), 7453-7467; https://doi.org/10.3390/e17117453 - 28 Oct 2015
Abstract
Consider a statistically-repeatable, shift-invariant system obeying an unknown probability law p(x) ≡ q2(x): Amplitude q(x) defines a source effect that is to be found. We show that q(x) may be found by considering [...] Read more.
Consider a statistically-repeatable, shift-invariant system obeying an unknown probability law p(x) ≡ q2(x): Amplitude q(x) defines a source effect that is to be found. We show that q(x) may be found by considering the flow of Fisher information J → I from source effect to observer that occurs during macroscopic observation of the system. Such an observation is irreversible and, hence, incurs a general loss I - J of the information. By requiring stability of the law q(x), as well, it is found to obey a principle I − J = min. of “extreme physical information” (EPI). Information I is the same functional of q(x) for any shift-invariant system, and J is a functional defining a physical source effect that must be known at least approximately. The minimum of EPI implies that I ≈ J or received information tends to well-approximate reality. Past applications of EPI to predicting laws of statistical physics, chemistry, biology, economics and social organization are briefly described. Full article
(This article belongs to the Special Issue Applications of Fisher Information in Sciences)
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