STATIONARITY AND INFERENCE IN MULTISTATE PROMOTER MODELS OF STOCHASTIC GENE EXPRESSION VIA STICK-BREAKING MEASURES

In a general stochastic multistate promoter model of dynamic messenger ribonucleic acid (mRNA)/protein interactions, we identify the stationary joint distribution of the promoter state, mRNA, and protein levels through an explicit ``stick-breaking"" construction perhaps of interest in itself. This derivation is a constructive advance over previous work where the stationary distribution is solved only in restricted cases. Moreover, the stick-breaking construction allows us to sample directly from the stationary distribution, permitting inference procedures and model selection. In this context, we discuss numerical Bayesian experiments to illustrate the results.