Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C(∗)-Algebras

A geometrical formulation of estimation theory for finite-dimensional [Formula: see text]-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer–Rao and Helstrom bounds for parametric stati...

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Autores principales: Ciaglia, Florio M., Jost, Jürgen, Schwachhöfer, Lorenz
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7712486/
https://www.ncbi.nlm.nih.gov/pubmed/33266515
http://dx.doi.org/10.3390/e22111332
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author Ciaglia, Florio M.
Jost, Jürgen
Schwachhöfer, Lorenz
author_facet Ciaglia, Florio M.
Jost, Jürgen
Schwachhöfer, Lorenz
author_sort Ciaglia, Florio M.
collection PubMed
description A geometrical formulation of estimation theory for finite-dimensional [Formula: see text]-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer–Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented.
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spelling pubmed-77124862021-02-24 Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C(∗)-Algebras Ciaglia, Florio M. Jost, Jürgen Schwachhöfer, Lorenz Entropy (Basel) Article A geometrical formulation of estimation theory for finite-dimensional [Formula: see text]-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer–Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented. MDPI 2020-11-23 /pmc/articles/PMC7712486/ /pubmed/33266515 http://dx.doi.org/10.3390/e22111332 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Ciaglia, Florio M.
Jost, Jürgen
Schwachhöfer, Lorenz
Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C(∗)-Algebras
title Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C(∗)-Algebras
title_full Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C(∗)-Algebras
title_fullStr Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C(∗)-Algebras
title_full_unstemmed Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C(∗)-Algebras
title_short Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C(∗)-Algebras
title_sort differential geometric aspects of parametric estimation theory for states on finite-dimensional c(∗)-algebras
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7712486/
https://www.ncbi.nlm.nih.gov/pubmed/33266515
http://dx.doi.org/10.3390/e22111332
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