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Title: A nonparametric Bayesian model for clustering inhomogeneous Poisson processes Authors:  Xiaowei Wu - Virginia Tech (United States) [presenting]
Hongxiao Zhu - Virginia Tech (United States)
Abstract: Random events arise in many applications and numerous data have been generated to record their distribution in time or space. A commonly used model for such data is the inhomogeneous Poisson process (IHPP), which is characterized by its time- or location-dependent intensity function. Motivated by a genomic application of identifying transcriptional regulatory modules using modern ChIP-seq data, we developed a nonparametric Bayesian clustering model for samples of multiple IHPPs. This model, called Dirichlet process mixture of log Gaussian Cox process (DPM-LGCP), employs a DP prior to the random distribution of the latent IHPP log intensity functions to facilitate clustering of functional data and the consequent IHPPs arising therefrom. To overcome the inference difficulty caused by calculating marginal likelihood of IHPP, we adopt approximate Bayesian inference based on integrated nested Laplace approximations (INLA), and integrate the approximated marginal likelihood into DPM sampling. Simulation studies show that DPM-LGCP achieves good accuracy and robustness and outperforms two alternative clustering methods. We apply this model to learn transcription factor binding patterns and identify transcriptional regulatory modules in mouse ES cells. Findings from such analysis help uncover how transcription factors work together in orchestrating gene activity in ES cells, and will eventually lead to a better understanding of different tissue development and disease progression.