Open Access
March 2019 Mixture Modeling on Related Samples by ψ-Stick Breaking and Kernel Perturbation
Jacopo Soriano, Li Ma
Bayesian Anal. 14(1): 161-180 (March 2019). DOI: 10.1214/18-BA1106


There has been great interest recently in applying nonparametric kernel mixtures in a hierarchical manner to model multiple related data samples jointly. In such settings several data features are commonly present: (i) the related samples often share some, if not all, of the mixture components but with differing weights, (ii) only some, not all, of the mixture components vary across the samples, and (iii) often the shared mixture components across samples are not aligned perfectly in terms of their kernel parameters such as the location and spread in Gaussian kernels, but rather display small misalignments either due to systematic cross-sample difference or more often due to uncontrolled, extraneous causes. Properly incorporating these features in mixture modeling will enhance the efficiency of inference, whereas ignoring them not only reduces efficiency but can jeopardize the validity of the inference due to issues such as confounding. We propose to use two techniques for incorporating these features in modeling related data samples using kernel mixtures. The first technique, called ψ-stick breaking, is a joint generative process for the mixing weights through the breaking of both a stick shared by all the samples for the components that do not vary in size across samples and an idiosyncratic stick for each sample for those components that do vary in size. The second technique is to imbue random perturbation into the kernels, thereby accounting for cross-sample misalignment. These techniques can be used either separately or together in both parametric and nonparametric kernel mixtures. We derive efficient Bayesian inference recipes based on Markov Chain Monte Carlo (MCMC) sampling for models featuring these techniques, and illustrate their work through both simulated data and a real flow cytometry data set in prediction/estimation and testing multi-sample differences.


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Jacopo Soriano. Li Ma. "Mixture Modeling on Related Samples by ψ-Stick Breaking and Kernel Perturbation." Bayesian Anal. 14 (1) 161 - 180, March 2019.


Published: March 2019
First available in Project Euclid: 19 April 2018

zbMATH: 07001979
MathSciNet: MR3910042
Digital Object Identifier: 10.1214/18-BA1106

Primary: 62F15 , 62G99
Secondary: 62G07

Keywords: Bayesian nonparametrics , clustering , flow cytometry , hierarchical models

Vol.14 • No. 1 • March 2019
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