Application of MCMC to dynamical systems. (A) A kinetic model with three states and four free parameters. (B) Time course of the population of state B. Curve was generated by solving the dynamical system in A with the parameters {a, b, r, s} = {15, 2, 6, 4} (values in s⁻¹). (C) MCMC results when inferring the parameter values from the data in B. Top panel shows one dimension of the Markov chain (corresponding to parameter a) throughout the course of the simulation (thick trace). Thin trace is the corresponding marginal likelihood, which quantifies the total goodness of fit between the model and the data. All movements of the chain after the marginal likelihood settles (∼100 iterations) generate iid samples from the posterior distribution. Lower traces are the corresponding trajectories for the remaining parameters. (D) Histograms of the marginal posterior distribution of each parameter shown along with the true values (vertical lines) and the corresponding 95% credible interval (horizontal line segment).