Restricted type II maximum likelihood priors on regression coefficients
In Bayesian hypothesis testing and model selection, prior distributions must be chosen carefully. For example, setting arbitrarily large prior scales for location parameters, which is common practice in estimation problems, can lead to undesirable behavior in testing (see Lindley’s paradox; Lindley...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/433737 |
| Acceso en línea: | https://hdl.handle.net/2117/433737 https://dx.doi.org/10.1214/19-ba1188 |
| Access Level: | acceso abierto |
| Palabra clave: | Mathematical statistics Estadística matemàtica Classificació AMS::62 Statistics::62F Parametric inference Àrees temàtiques de la UPC::Matemàtiques i estadística::Estadística matemàtica::Inferència estadística |
| Sumario: | In Bayesian hypothesis testing and model selection, prior distributions must be chosen carefully. For example, setting arbitrarily large prior scales for location parameters, which is common practice in estimation problems, can lead to undesirable behavior in testing (see Lindley’s paradox; Lindley (1957)). We study the properties of some restricted type II maximum likelihood (type II ML) priors on regression coefficients. In type II ML, hyperparameters are “estimated” by maximizing the marginal likelihood of a model. In this article, we define priors by estimating their variances or covariance matrices, adding restrictions which ensure that the resulting priors are at least as vague as conventional proper priors for model uncertainty. We find that these type II ML priors typically yield results that are close to answers obtained with the Bayesian Information Criterion (BIC; Schwarz (1978)). |
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