Bayesian estimation for quantification by real-time Polymerase Chain Reaction
The aim of Quantitative Polymerase Chain Reaction is to determine the initial amount $X_0$ 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 $\{p_n\}_n$ of replication of the molecules, $p_n$ being the probability that a molecule will duplicate at replication cycle $n$. Assuming $p_n=p$ for all $n$, we propose to estimate the unknown parameter $\theta=(p, X_0)$ in a Bayesian framework under a Bienaym\'e-Galton-Watson branching model of the amplification process. The Bayesian approach allows us to take into account some prior information on the parameter. We build and study Bayesian estimators and sets of credibility of the parameter by Markov Chain Monte Carlo methods.