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Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems

Model selection criteria are widely used to identify the model that best represents the data among a set of potential candidates. Amidst the different model selection criteria, the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) are the most popular and better underst...

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Autores principales: Spolladore, Luca, Gelfusa, Michela, Rossi, Riccardo, Murari, Andrea
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8464864/
https://www.ncbi.nlm.nih.gov/pubmed/34573827
http://dx.doi.org/10.3390/e23091202
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author Spolladore, Luca
Gelfusa, Michela
Rossi, Riccardo
Murari, Andrea
author_facet Spolladore, Luca
Gelfusa, Michela
Rossi, Riccardo
Murari, Andrea
author_sort Spolladore, Luca
collection PubMed
description Model selection criteria are widely used to identify the model that best represents the data among a set of potential candidates. Amidst the different model selection criteria, the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) are the most popular and better understood. In the derivation of these indicators, it was assumed that the model’s dependent variables have already been properly identified and that the entries are not affected by significant uncertainties. These are issues that can become quite serious when investigating complex systems, especially when variables are highly correlated and the measurement uncertainties associated with them are not negligible. More sophisticated versions of this criteria, capable of better detecting spurious relations between variables when non-negligible noise is present, are proposed in this paper. Their derivation is obtained starting from a Bayesian statistics framework and adding an a priori Chi-squared probability distribution function of the model, dependent on a specifically defined information theoretic quantity that takes into account the redundancy between the dependent variables. The performances of the proposed versions of these criteria are assessed through a series of systematic simulations, using synthetic data for various classes of functions and noise levels. The results show that the upgraded formulation of the criteria clearly outperforms the traditional ones in most of the cases reported.
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spelling pubmed-84648642021-09-27 Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems Spolladore, Luca Gelfusa, Michela Rossi, Riccardo Murari, Andrea Entropy (Basel) Article Model selection criteria are widely used to identify the model that best represents the data among a set of potential candidates. Amidst the different model selection criteria, the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) are the most popular and better understood. In the derivation of these indicators, it was assumed that the model’s dependent variables have already been properly identified and that the entries are not affected by significant uncertainties. These are issues that can become quite serious when investigating complex systems, especially when variables are highly correlated and the measurement uncertainties associated with them are not negligible. More sophisticated versions of this criteria, capable of better detecting spurious relations between variables when non-negligible noise is present, are proposed in this paper. Their derivation is obtained starting from a Bayesian statistics framework and adding an a priori Chi-squared probability distribution function of the model, dependent on a specifically defined information theoretic quantity that takes into account the redundancy between the dependent variables. The performances of the proposed versions of these criteria are assessed through a series of systematic simulations, using synthetic data for various classes of functions and noise levels. The results show that the upgraded formulation of the criteria clearly outperforms the traditional ones in most of the cases reported. MDPI 2021-09-11 /pmc/articles/PMC8464864/ /pubmed/34573827 http://dx.doi.org/10.3390/e23091202 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/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 (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Spolladore, Luca
Gelfusa, Michela
Rossi, Riccardo
Murari, Andrea
Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems
title Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems
title_full Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems
title_fullStr Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems
title_full_unstemmed Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems
title_short Improved Treatment of the Independent Variables for the Deployment of Model Selection Criteria in the Analysis of Complex Systems
title_sort improved treatment of the independent variables for the deployment of model selection criteria in the analysis of complex systems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8464864/
https://www.ncbi.nlm.nih.gov/pubmed/34573827
http://dx.doi.org/10.3390/e23091202
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