A Bayesian approach of Quantitative Polymerase Chain Reaction
Quantitative Polymerase Chain Reaction aims at determining the initial amount $X_0$ of a specific portion of DNA molecules from the observation of the amplification process of the DNA molecules quantity. This amplification process is achieved through successive replication cycles. It depends on the efficiency $\{p_n\}_n$ of the replication of the molecules, $p_n$ being the probability that a molecule will duplicate at replication cycle $n$. Modelling the amplification process by a branching process and assuming $p_n=p$ for all $n$, we estimate the unknown parameter $\theta=(p, X_0)$ using Markov Chain Monte Carlo methods under a Bayesian framework.