Bayesian Estimation for Quantification by Real-time Polymerase Chain Reaction Under a Branching Process Model of the DNA Molecules Amplification Process

The aim of Quantitative Polymerase Chain Reaction is to determine the initial amount X0 of specific nucleic acids from an observed trajectory of the amplification process, the amplification being achieved through successive replication cycles. This process depends on the efficiency {pn}n of replication of the DNA molecules, pn being the probability that a molecule will duplicate at replication cycle n. Assuming pn = p for all n, Bayesian estimators of the unknown parameter θ = (p, X0) are constructed by Markov Chain Monte Carlo methods under a Bienayme-Galton-Watson branching model of the amplification process. The Bayesian approach takes into account some prior information on the parameter. Relying on simulated data, the proposed Bayesian estimators and their credibility sets are shown to be quite accurate.