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Bayesian analysis for mixtures of discrete distributions with a non-parametric component

Author

Listed:
  • Baba B. Alhaji
  • Hongsheng Dai
  • Yoshiko Hayashi
  • Veronica Vinciotti
  • Andrew Harrison
  • Berthold Lausen

Abstract

Bayesian finite mixture modelling is a flexible parametric modelling approach for classification and density fitting. Many areas of application require distinguishing a signal from a noise component. In practice, it is often difficult to justify a specific distribution for the signal component; therefore, the signal distribution is usually further modelled via a mixture of distributions. However, modelling the signal as a mixture of distributions is computationally non-trivial due to the difficulties in justifying the exact number of components to be used and due to the label switching problem. This paper proposes the use of a non-parametric distribution to model the signal component. We consider the case of discrete data and show how this new methodology leads to more accurate parameter estimation and smaller false non-discovery rate. Moreover, it does not incur the label switching problem. We show an application of the method to data generated by ChIP-sequencing experiments.

Suggested Citation

  • Baba B. Alhaji & Hongsheng Dai & Yoshiko Hayashi & Veronica Vinciotti & Andrew Harrison & Berthold Lausen, 2016. "Bayesian analysis for mixtures of discrete distributions with a non-parametric component," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1369-1385, June.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:8:p:1369-1385
    DOI: 10.1080/02664763.2015.1100594
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