Estimating the model evidence - or mariginal likelihood of the data - is a notoriously difficult task for finite and infinite mixture models and we reexamine here different Monte Carlo techniques advocated in the recent literature, as well as novel approaches based on Geyer (1994) reverse logistic regression technique, Chib (1995) algorithm, and Sequential Monte Carlo (SMC). Applications are numerous. In particular, testing for the number of components in a finite mixture model or against the fit of a finite mixture model for a given dataset has long been and still is an issue of much interest, albeit yet missing a fully satisfactory resolution. Using a Bayes factor to find the right number of components K in a finite mixture model is known to provide a consistent procedure. We furthermore establish the consistence of the Bayes factor when comparing a parametric family of finite mixtures against the nonparametric 'strongly identifiable' Dirichlet Process Mixture (DPM) model.

翻译：估计模型证据 -- -- 即数据的几何可能性 -- -- 对于有限和无限混合模型来说,是一项极为困难的任务,我们在此重新审查最近文献中倡导的不同蒙特卡洛技术,以及基于Geryer(1994年)逆向后勤回归技术、Chib(1995年)算法和序列蒙特卡洛(SMC)的新办法。应用是众多的。特别是,试验有限混合物模型中的成分数量或对照某一数据集的有限混合物模型是否适合使用有限混合物模型的问题,过去和现在都是一个非常令人感兴趣的问题,尽管还缺少一个完全令人满意的解决办法。使用一个贝斯系数来寻找有限混合物模型中K成分的正确数量,可以提供一致的程序。我们进一步确定,在比较非参数性“可明显识别”的Drichlet进程混合模型(DPM)时,对定型混合物的参数组群进行了比较。