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dc.contributor.author
Hernández Lahme, Damián Gabriel
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dc.contributor.author
Samengo, Ines
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dc.date.available
2023-02-15T19:17:42Z
dc.date.issued
2022-01
dc.identifier.citation
Hernández Lahme, Damián Gabriel; Samengo, Ines; Inferring a Property of a Large System from a Small Number of Samples; Molecular Diversity Preservation International; Entropy; 24; 1; 1-2022; 1-17
dc.identifier.issn
1099-4300
dc.identifier.uri
http://hdl.handle.net/11336/188161
dc.description.abstract
Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the knowledge of the prior distribution, and in many situations, it is not clear which prior should be used. Several estimators have been developed so far in which the proposed prior us individually tailored for each property of interest; such is the case, for example, for the entropy, the amount of mutual information, or the correlation between pairs of variables. In this paper, we propose a general framework to select priors that is valid for arbitrary properties. We first demonstrate that only certain aspects of the prior distribution actually affect the inference process. We then expand the sought prior as a linear combination of a one-dimensional family of indexed priors, each of which is obtained through a maximum entropy approach with constrained mean values of the property under study. In many cases of interest, only one or very few components of the expansion turn out to contribute to the Bayesian estimator, so it is often valid to only keep a single component. The relevant component is selected by the data, so no handcrafted priors are required. We test the performance of this approximation with a few paradigmatic examples and show that it performs well in comparison to the ad-hoc methods previously proposed in the literature. Our method highlights the connection between Bayesian inference and equilibrium statistical mechanics, since the most relevant component of the expansion can be argued to be that with the right temperature.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Molecular Diversity Preservation International
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by/2.5/ar/
dc.subject
BAYESIAN
dc.subject
ENTROPY
dc.subject
INFERENCE
dc.subject
MUTUAL INFORMATION
dc.subject
UNDERSAMPLED
dc.subject.classification
Otras Ciencias Físicas
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dc.subject.classification
Ciencias Físicas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.subject.classification
Estadística y Probabilidad
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Inferring a Property of a Large System from a Small Number of Samples
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2023-02-09T15:44:36Z
dc.journal.volume
24
dc.journal.number
1
dc.journal.pagination
1-17
dc.journal.pais
Suiza
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dc.journal.ciudad
Basilea
dc.description.fil
Fil: Hernández Lahme, Damián Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina
dc.description.fil
Fil: Samengo, Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina
dc.journal.title
Entropy
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/1099-4300/24/1/125/htm
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.3390/e24010125
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