论文标题
有限和无限混合模型和应用中的证据估计
Evidence estimation in finite and infinite mixture models and applications
论文作者
论文摘要
估计模型证据 - 或数据的大型可能性 - 对于有限和无限混合模型而言，这是一项艰巨的任务，我们在最近的文献中倡导了不同的蒙特卡洛技术，以及基于Geyer（1994）的新方法，基于Geyer（1994）反向逻辑回归技术；申请很多。特别是，对有限混合模型中的组件数量或针对给定数据集的有限混合模型的拟合度进行了测试一直是一个非常有趣的问题，尽管却缺少完全令人满意的分辨率。已知使用贝叶斯因子在有限混合物模型中找到合适数量的组件k可以提供一致的程序。当比较有限混合物的参数家族与非参数“可识别的” Dirichlet工艺混合物（DPM）模型时，我们还建立了贝叶斯因子的一致性。
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.
