Generalized species sampling priors with latent Beta reinforcements.
Generalized species sampling priors with latent Beta reinforcements.
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DOI：
10.1080/01621459.2014.950735
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发表时间：
2014-12-01
影响因子：
3.7
通讯作者：
Guindani M
中科院分区：
文献类型：
--
作者：
Airoldi EM;Costa T;Bassetti F;Leisen F;Guindani M
许多流行的贝叶斯非参数先验可以用可交换物种采样序列来表征。然而，在某些应用中，可交换性可能不合适。我们引入了一种新颖且概率一致的不可交换物种采样序列家族，其特征是易于处理的预测概率函数，其权重由一系列独立的 Beta 随机变量驱动。我们将它们的理论聚类特性与狄利克雷过程和双参数泊松-狄利克雷过程进行了比较。与现有工作不同，拟议的结构提供了联合过程的完整特征。然后，我们建议在分层贝叶斯建模框架中使用先验分布等过程，并描述用于后验推理的马尔可夫链蒙特卡罗采样器。我们在模拟研究中评估先验的性能和所得推理的稳健性，并与流行的狄利克雷过程混合物和隐马尔可夫模型进行比较。最后，我们开发了一种利用阵列 CGH 数据检测乳腺癌染色体畸变的应用程序。
Many popular Bayesian nonparametric priors can be characterized in terms of exchangeable species sampling sequences. However, in some applications, exchangeability may not be appropriate. We introduce a novel and probabilistically coherent family of non-exchangeable species sampling sequences characterized by a tractable predictive probability function with weights driven by a sequence of independent Beta random variables. We compare their theoretical clustering properties with those of the Dirichlet Process and the two parameters Poisson-Dirichlet process. The proposed construction provides a complete characterization of the joint process, differently from existing work. We then propose the use of such process as prior distribution in a hierarchical Bayes modeling framework, and we describe a Markov Chain Monte Carlo sampler for posterior inference. We evaluate the performance of the prior and the robustness of the resulting inference in a simulation study, providing a comparison with popular Dirichlet Processes mixtures and Hidden Markov Models. Finally, we develop an application to the detection of chromosomal aberrations in breast cancer by leveraging array CGH data.
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