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Combinatorial Mixtures of Multiparameter Distributions: An Application to Bivariate Data

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  • Edefonti Valeria

    (Department of Clinical Sciences and Community Health, University of Milan, via A. Vanzetti, 5 , Milan, MI 20133, Italy)

  • Parmigiani Giovanni

    (Department of Biostatistics and Computational Biology, Dana-Farber Cancer Institute, Boston, MA, USA; Department of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA, USA)

Abstract

We introduce combinatorial mixtures – a flexible class of models for inference on mixture distributions whose components have multidimensional parameters. The key idea is to allow each element of the component-specific parameter vectors to be shared by a subset of other components. This approach allows for mixtures that range from very flexible to very parsimonious and unifies inference on component-specific parameters with inference on the number of components. We develop Bayesian inference and computational approaches for this class of distributions, and illustrate them in an application. This work was originally motivated by the analysis of cancer subtypes: in terms of biological measures of interest, subtypes may be characterized by differences in location, scale, correlations or any of the combinations. We illustrate our approach using publicly available data on molecular subtypes of lung and prostate cancers.

Suggested Citation

  • Edefonti Valeria & Parmigiani Giovanni, 2017. "Combinatorial Mixtures of Multiparameter Distributions: An Application to Bivariate Data," The International Journal of Biostatistics, De Gruyter, vol. 13(1), pages 1-31, May.
    • Handle: RePEc:bpj:ijbist:v:13:y:2017:i:1:p:31:n:1
    DOI: 10.1515/ijb-2015-0064
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    References listed on IDEAS

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    1. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    2. repec:dau:papers:123456789/6069 is not listed on IDEAS
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