In the human genome, susceptibility to common diseases is likely to be determined by interactions between multiple genetic variants. We propose an innovative Bayesian method to tackle the challenging problem of multi-locus pattern selection in the case of quantitative phenotypes. For the first time, in this domain, a whole Bayesian theoretical framework has been defined to incorporate additional transcriptomic knowledge. Thus we fully integrate the relationships between phenotypes, transcripts (messenger RNAs) and genotypes. Within this framework, the relationship between the genetic variants and the quantitative phenotype is modeled through a multivariate linear model. The posterior distribution on the parameter space can not be estimated through direct calculus. Therefore we design an algorithm based on Markov Chain Monte Carlo (MCMC) methods. In our case, the number of putative transcripts involved in the disease is unknown. Moreover, this dimension parameter is not fixed. To cope with trans-dimensional moves, our sampler is designed as a reversible jump MCMC (RJMCMC). In this document, we establish the whole theoretical background necessary to design this specific RJMCMC.