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Title: Objective Bayesian model choice for non-nested families: the case of the Poisson and the negative binomial
Authors: Moreno, Elías
Martínez, Carmen
Vázquez Polo, Francisco José 
UNESCO Clasification: 530204 Estadística económica
Keywords: Bayesian Model Selection
Rate Of Convergence
Sampling Behavior For Small Sample Sizes
Test For Separate Families
Issue Date: 2021
Journal: Test 
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(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.
ISSN: 1133-0686
DOI: 10.1007/s11749-020-00717-z
Source: Test[ISSN 1133-0686], n. 30, p. 255–273
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