Bayesian analysis of single‐molecule experimental data

Summary. Recent advances in experimental technologies allow scientists to follow biochemical processes on a single‐molecule basis, which provides much richer information about chemical dynamics than traditional ensemble‐averaged experiments but also raises many new statistical challenges. The paper provides the first likelihood‐based statistical analysis of the single‐molecule fluorescence lifetime experiment designed to probe the conformational dynamics of a single deoxyribonucleic acid (DNA) hairpin molecule. The conformational change is initially treated as a continuous time two‐state Markov chain, which is not observable and must be inferred from changes in photon emissions. This model is further complicated by unobserved molecular Brownian diffusions. Beyond the simple two‐state model, a competing model that models the energy barrier between the two states of the DNA hairpin as an Ornstein–Uhlenbeck process has been suggested in the literature. We first derive the likelihood function of the simple two‐state model and then generalize the method to handle complications such as unobserved molecular diffusions and the fluctuating energy barrier. The data augmentation technique and Markov chain Monte Carlo methods are developed to sample from the posterior distribution desired. The Bayes factor calculation and posterior estimates of relevant parameters indicate that the fluctuating barrier model fits the data better than the simple two‐state model.