A Bayesian HMM with random effects and an unknown number of states for DNA copy number analysis

Abstract

Hidden Markov models (HMMs) have been shown to be a flexible tool for modelling complex biological processes. However, choosing the number of hidden states remains an open question and the inclusion of random effects also deserves more research, as it is a recent addition to the fixed-effect HMM in many application fields. We present a Bayesian mixed HMM with an unknown number of hidden states and fixed covariates. The model is fitted using reversible-jump Markov chain Monte Carlo, avoiding the need to select the number of hidden states. We show through simulations that the estimations produced are more precise than those from a fixed-effect HMM and illustrate its practical application to the analysis of DNA copy number data, a field where HMMs are widely used.

Keywords:

• array comparative genomic hybridization
• Bayesian inference
• copy number variation
• hidden Markov models
• reversible-jump Markov chain Monte Carlo

AMS Subject Classification: :

• 62F15
• 62M05
• 62P10

Acknowledgements

This research was supported by the Spanish Ministerio de Ciencia e Innovación (grants MTM 2009-11161 and BIO2009-12458) and Fundación de Investigación Médica Mutua Madrileña. We want to thank an anonymous reviewer for his comments that improved the quality of the paper.