Objective Bayesian model choice for non-nested families: the case of the Poisson and the negative binomial

Elías Moreno (), Carmen Martínez () and Francisco–José Vázquez–Polo ()
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Elías Moreno: University of Granada
Carmen Martínez: University of Granada
Francisco–José Vázquez–Polo: University of Las Palmas de Gran Canaria

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2021, vol. 30, issue 1, No 15, 255-273

Abstract: Abstract 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 $$O(a^{n})$$ O ( a n ) , $$a>1$$ 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 $$r=1,\ldots ,L$$ 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.

Keywords: Bayesian model selection; Test for separate families; Consistency; Sampling behavior for small sample sizes; Rate of convergence; 62F15; 62F03; 62P05 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11749-020-00717-z

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