Abstract:    The detection and location in DNA of transcription factor binding sites is a problem within functional genomics which has not yet been solved. The first generation of prediction-algorithms was searching for one motif at a time. This is successful in bacteria and lower eukaryotes like yeast, but fails in higher eukaryotes like mice or humans. More factors work together there, which lowers the SNR under which the algorithms have to work. A solution can be to search for specific combinations of motifs (modules) which influence together the expression of a gene. This project wants to model the modules with Hidden Markov Models, based on their successful application in other sequence-modeling domains. Existing training algorithms suffer from local optima. These local optima might be sufficient for other applications, but are quite useless for our purpose. Therefore Markov Chain Monte Carlo methods are developed for HMMs in a Bayesian framework. They have proven their value in similar applications. The final aim of the project is to create a theoretical probabilistic framework and practical (software) platform for Cis-Regulatory Module Discovery which will be validated on a case study about heart failure.