Generalized species sampling priors with latent Beta reinforcements

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.

A Nonparametric Bayesian Model for Local Clustering with Application to Proteomics

We propose a nonparametric Bayesian local clustering (NoB-LoC) approach for heterogeneous data. NoB-LoC implements inference for nested clusters as posterior inference under a Bayesian model. Using protein expression data as an example, the NoB-LoC model defines a protein (column) cluster as a set of proteins that give rise to the same partition of the samples (rows). In other words, the sample partitions are nested within protein clusters. The common clustering of the samples gives meaning to the protein clusters. Any pair of samples might belong to the same cluster for one protein set but to different clusters for another protein set. These local features are different from features obtained by global clustering approaches such as hierarchical clustering, which create only one partition of samples that applies for all the proteins in the data set. In addition, the NoB-LoC model is different from most other local or nested clustering methods, which define clusters based on common parameters in the sampling model. As an added and important feature, the NoB-LoC method probabilistically excludes sets of irrelevant proteins and samples that do not meaningfully co-cluster with other proteins and samples, thus improving the inference on the clustering of the remaining proteins and samples. Inference is guided by a joint probability model for all the random elements. We provide a simulation study and a motivating example to demonstrate the unique features of the NoB-LoC model.