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

Bayesian finite mixture modelling is a flexible parametric modelling approach for classification and density fitting. Many application areas 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 challenging due to the difficulties in justifying the exact number of components to be used and due to the label-switching problem. The use of a non-parametric distribution to model the signal component is proposed. This new methodology leads to more accurate parameter estimation, smaller classification error rate and smaller false non-discovery rate in the case of discrete data. Moreover, it does not incur the label-switching problem. An application of the method to data generated by ChIP-sequencing experiments is shown. A one-dimensional Markov random field model is proposed, which accounts for the spatial dependencies in the data. The methodology is also applied to ChIP-seq data, which shows that the new method detected more genes enriched regions than similar existing methods at the same false discovery rate.