Objective Bayesian model choice for non-nested families:: the case of the Poisson and the negative binomial
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Elías Moreno [1] ; Carmen Martínez [1] ; Francisco José Vázquez Polo [2]
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[1] Universidad de Granada
Universidad de Granada
Granada, España
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[2] Universidad de Las Palmas de Gran Canaria
Universidad de Las Palmas de Gran Canaria
Gran Canaria, España
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- Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 30, Nº. 1, 2021, págs. 255-273
- Idioma: inglés
- DOI: 10.1007/s11749-020-00717-z
- Texto completo no disponible (Saber más ...)
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Resumen
Selecting a statistical model from a set of competing models is a central issue in the scientific task, and the Bayesian approach to model selection is based on the posterior model distribution, a quantification of the updated uncertainty on the entertained models. We present a Bayesian procedure for choosing a family between the Poisson and the geometric families and prove that the procedure is consistent with rate O(an), a>1, where a is a function of the parameter of the true model. An extension of this procedure to the multiple testing Poisson and negative binomial with r successes for r=1,…,L is also proved to be consistent with exponential rate. For small sample sizes, a simulation study indicates that the model selection between the above distributions is made with large uncertainty when sampling from a specific subset of distributions. This difficulty is however mitigated by the large consistency rate of the procedure.
