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

Baba B. Alhaji, Hongsheng Dai, Yoshiko Hayashi, Veronica Vinciotti, Andrew Harrison and Berthold Lausen

Journal of Applied Statistics, 2016, vol. 43, issue 8, 1369-1385

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.

Date: 2016
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DOI: 10.1080/02664763.2015.1100594

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