Chebyshevskii Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Chebyshevskii Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Chebyshevskii Sb., 2015, Volume 16, Issue 4, Pages 28–40 (Mi cheb434)  

Statistic structure generated by randomize density

I. I. Bavrina, V. I. Panzhenskyb, O. E. Iaremkob

a Moscow State Pedagogical University
b Penza State University

Abstract: Differential geometry methods of have applications in the information files study (families of probability distributions of spaces of quantum states, neural networks, etc.). Research on geometry information back to the S. Rao that based by Fisher information matrix defined the Riemannian metric of probability distributions manifold. Further investigation led to the concept of statistical manifold. Statistical manifold is a smooth finite-dimensional manifold on which a metrically-affine structure, ie, metric and torsion-free linear connection that is compatible with a given metric; while the condition Codazzi. Geometric manifold and the manifold is given statistical structure tensor.
In the present study examines the statistical structure of the generated randomized density of the normal distribution and the Cauchy distribution. The study put the allegation that a randomized probability density of the normal distribution can be regarded as the solution of the Cauchy problem for the heat equation, and randomized probability density of the Cauchy distribution can be considered as a solution to the Dirichlet problem for the Laplace equation. Conversely, the solution of the Cauchy problem for the heat equation can be regarded as a randomized probability density of the normal distribution, and the solution of the Dirichlet problem for the Laplace equation as randomized probability density of the Cauchy distribution. The main objective of the study was the fact that for each of these two cases to find the Fisher information matrix components and structural tensor.
We found nonlinear differential equations of the first, second and third order for the density of the normal distribution and Cauchy density computational difficulties to overcome. The components of the metric tensor (the Fisher information matrix) and the components of the strain tensor are calculated according to formulas in which there is the log-likelihood function, ie, logarithm of the density distribution. Because of the positive definiteness of the Fisher information matrix obtained inequality, which obviously satisfy the Cauchy problem solution with nonnegative initial conditions in the case of the Laplace equation and the heat equation.
Bibliography: 23 titles.

Keywords: Fisher information matrix, structure tensor, random density, Poisson formula, Heat equation, Dirichlet problem, Laplace equation.

Full text: PDF file (238 kB)
References: PDF file   HTML file
UDC: 514.7,517.9
Received: 09.11.2015

Citation: I. I. Bavrin, V. I. Panzhensky, O. E. Iaremko, “Statistic structure generated by randomize density”, Chebyshevskii Sb., 16:4 (2015), 28–40

Citation in format AMSBIB
\Bibitem{BavPanYar15}
\by I.~I.~Bavrin, V.~I.~Panzhensky, O.~E.~Iaremko
\paper Statistic structure generated by randomize density
\jour Chebyshevskii Sb.
\yr 2015
\vol 16
\issue 4
\pages 28--40
\mathnet{http://mi.mathnet.ru/cheb434}
\elib{https://elibrary.ru/item.asp?id=25006092}


Linking options:
  • http://mi.mathnet.ru/eng/cheb434
  • http://mi.mathnet.ru/eng/cheb/v16/i4/p28

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Number of views:
    This page:216
    Full text:70
    References:76

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021