POWER LAWS DISTRIBUTIONS IN OBJECTIVE PRIORS

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dc.contributor.authorRamos, Pedro Luiz
dc.contributor.authorRodrigues, Francisco A.
dc.contributor.authorRamos, Eduardo
dc.contributor.authorDey, Dipak K.
dc.contributor.authorLouzada, Francisco
dc.date.accessioned2025-01-20T17:17:16Z
dc.date.available2025-01-20T17:17:16Z
dc.date.issued2023
dc.description.abstractUsing objective priors in Bayesian applications has become a common way of analyzing data without using subjective information. Formal rules are usually used to obtain these prior distributions, and the data provide the dominant infor-mation in the posterior distribution. However, these priors are typically improper, and may lead to an improper posterior. Here, for a general family of distribu-tions, we show that the objective priors obtained for the parameters either follow a power law distribution, or exhibit asymptotic power law behavior. As a result, we observe that the exponents of the model are between 0.5 and 1. Understand-ing this behavior allows us to use the exponent of the power law directly to verify whether such priors lead to proper or improper posteriors. The general family of distributions we consider includes essential models such as the exponential, gamma, Weibull, Nakagami-m, half-normal, Rayleigh, Erlang, and Maxwell Boltzmann dis-tributions, among others. In summary, we show that understanding the mechanisms that describe the shape of a prior provides essential information that can be used to understand the properties of posterior distributions.
dc.fuente.origenWOS
dc.identifier.doi10.5705/ss.202020.0521
dc.identifier.eissn1996-8507
dc.identifier.issn1017-0405
dc.identifier.urihttps://doi.org/10.5705/ss.202020.0521
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/91354
dc.identifier.wosidWOS:001107595000006
dc.issue.numero3
dc.language.isoen
dc.pagina.final1984
dc.pagina.inicio1959
dc.revistaStatistica sinica
dc.rightsacceso restringido
dc.subjectBayesian inference
dc.subjectobjective prior
dc.subjectpower-law
dc.titlePOWER LAWS DISTRIBUTIONS IN OBJECTIVE PRIORS
dc.typeartículo
dc.volumen33
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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