A Hybrid Parameter Estimation Algorithm for Beta Mixtures and Applications to Methylation State Classification
Mixtures of beta distributions have previously been shown to be a flexible tool for modeling data with values on the unit interval, such as methylation levels. However, maximum likelihood parameter estimation with beta distributions suffers from problems because of singularities in the log-likelihood function if some observations take the values 0 or 1. While ad-hoc corrections have been proposed to mitigate this problem, we propose a different approach to parameter estimation for beta mixtures where such problems do not arise in the first place. Our algorithm has computational advantages over the maximum-likelihood-based EM algorithm. As an application, we demonstrate that methylation state classification is more accurate when using adaptive thresholds from beta mixtures than non-adaptive thresholds on observed methylation levels.
KeywordsMixture model Beta distribution Maximum likelihood Method of moments EM algorithm Differential methylation Classification
C.S. acknowledges funding from the Federal Ministry of Education and Research (BMBF) under the Project Number 01KU1216 (Deutsches Epigenom Programm, DEEP). S.R. acknowledges funding from the Mercator Research Center Ruhr (MERCUR), project Pe-2013-0012 (UA Ruhr professorship) and from the German Research Foundation (DFG), Collaborative Research Center SFB 876, project C1.