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

从一组竞争模型中选择统计模型是科学任务中的中心问题，而贝叶斯模型选择方法基于后验模型分布，即对娱乐模型上更新的不确定性的量化。我们提出了一种用于在Poisson和几何族之间选择族的贝叶斯方法，并证明该过程与速率\（O（a ^ {n}）\），\（a> 1 \）一致，其中a是a真实模型参数的函数。此过程扩展到\（r = 1，\ ldots，L \）的r次成功的多重测试泊松和负二项式也被证明与指数率一致。对于小样本量，仿真研究表明，从特定分布子集进行采样时，上述分布之间的模型选择具有较大的不确定性。但是，该过程的高一致性降低了这一困难。