Abstract

Repulsive mixture models have recently gained popularity for Bayesian cluster detection. Compared to more traditional mixture models, repulsive mixture models produce a smaller number of well-separated clusters. The most commonly used methods for posterior inference either require to fix a priori the number of components or are based on reversible jump MCMC computation. We present a general framework for mixture models, when the prior of the “cluster centers” is a finite repulsive point process depending on a hyperparameter, specified by a density which may depend on an intractable normalizing constant. By investigating the posterior characterization of this class of mixture models, we derive a MCMC algorithm which avoids the well-known difficulties associated to reversible jump MCMC computation. In particular, we use an ancillary variable method, which eliminates the problem of having intractable normalizing constants in the Hastings ratio. The ancillary variable method relies on a perfect simulation algorithm, and we demonstrate this is fast because the number of components is typically small. In several simulation studies and an application on sociological data, we illustrate the advantage of our new methodology over existing methods, and we compare the use of a determinantal or a repulsive Gibbs point process prior model. Supplementary files for this article are available online.

摘要

排斥混合模型最近在贝叶斯聚类检测中广受欢迎。与更传统的混合模型相比，排斥混合模型产生较少数量的良好分离的簇。最常用的后验推理方法要么需要先验确定组件的数量，要么基于可逆跳跃 MCMC 计算。我们提出了混合模型的一般框架，当“簇中心”的先验是取决于超参数的有限排斥点过程，由密度指定，该密度可能取决于难以处理的归一化常数。通过研究这类混合模型的后验特征，我们推导出了一种 MCMC 算法，该算法避免了与可逆跳跃 MCMC 计算相关的众所周知的困难。特别是，我们使用辅助变量方法，这消除了在黑斯廷斯比率中具有难以处理的归一化常数的问题。辅助变量方法依赖于完美的模拟算法，我们证明这很快，因为组件的数量通常很少。在几项模拟研究和社会学数据的应用中，我们说明了我们的新方法相对于现有方法的优势，并且我们比较了行列式或排斥性吉布斯点过程先验模型的使用。本文的补充文件可在线获取。在几项模拟研究和社会学数据的应用中，我们说明了我们的新方法相对于现有方法的优势，并且我们比较了行列式或排斥性吉布斯点过程先验模型的使用。本文的补充文件可在线获取。在几项模拟研究和社会学数据的应用中，我们说明了我们的新方法相对于现有方法的优势，并且我们比较了行列式或排斥性吉布斯点过程先验模型的使用。本文的补充文件可在线获取。