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.
Highlights
Introduction and motivationFinite mixture modelling can be used to describe data obtained from different populations
In the last two decades, many new methodologies have been proposed for the Bayesian analysis of finite mixture models, such as Diebolt and Robert (1994), West
The existing literature has shown that finite mixture models can be inferred in a simple and effective way in a Bayesian estimation framework, persistent challenges still exist in the diagnostic of Markov Chain Monte Carlo (MCMC) convergence due to the following aspects
Summary
Finite mixture modelling can be used to describe data obtained from different populations. Many authors have devised different methodologies for estimating the number of components in a Bayesian finite mixture models, for example reversible jump MCMC (Richardson and Green, 1997) and Birth and Death MCMC (Stephens, 2000a; Nobile et al, 2007). Another approach to deal with the unknown number of components is to use a mixture of Dirichlet processes (Antoniak, 1974; Escobar and West, 1995), which allows an infinite number of components. This motivates our study, as we discuss in detail in the following subsection
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