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Abstract We develop a prior probability model for temporal Poisson process intensities through structured mixtures of Erlang densities with common scale parameter, mixing on the integer shape parameters. The mixture weights are constructed through increments of a cumulative intensity function which is modeled nonparametrically with a gamma process prior. Such model specification provides a novel extension of Erlang mixtures for density estimation to the intensity estimation setting. The prior model structure supports general shapes for the point process intensity function, and it also enables effective handling of the Poisson process likelihood normalizing term resulting in efficient posterior simulation. The Erlang mixture modeling approach is further elaborated to develop an inference method for spatial Poisson processes. The methodology is examined relative to existing Bayesian nonparametric modeling approaches, including empirical comparison with Gaussian process prior based models, and is illustrated with synthetic and real data examples.
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Two‐group Poisson‐Dirichlet mixtures for multiple testing
Abstract The simultaneous testing of multiple hypotheses is common to the analysis of high‐dimensional data sets. The two‐group model, first proposed by Efron, identifies significant comparisons by allocating observations to a mixture of an empirical null and an alternative distribution. In the Bayesian nonparametrics literature, many approaches have suggested using mixtures of Dirichlet Processes in the two‐group model framework. Here, we investigate employing mixtures of two‐parameter Poisson‐Dirichlet Processes instead, and show how they provide a more flexible and effective tool for large‐scale hypothesis testing. Our model further employs nonlocal prior densities to allow separation between the two mixture components. We obtain a closed‐form expression for the exchangeable partition probability function of the two‐group model, which leads to a straightforward Markov Chain Monte Carlo implementation. We compare the performance of our method for large‐scale inference in a simulation study and illustrate its use on both a prostate cancer data set and a case‐control microbiome study of the gastrointestinal tracts in children from underdeveloped countries who have been recently diagnosed with moderate‐to‐severe diarrhea.
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- Award ID(s):
- 1659921
- PAR ID:
- 10451041
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Biometrics
- Volume:
- 77
- Issue:
- 2
- ISSN:
- 0006-341X
- Format(s):
- Medium: X Size: p. 622-633
- Size(s):
- p. 622-633
- Sponsoring Org:
- National Science Foundation
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