(color online) The optimization algorithm applies to simulation of simple two-state transitions. (a) State time trace obtained by Monte Carlo simulation with parameters and . (b) Folding and unfolding rates obtained by the traditional mean dwell time method are shown as functions of the average transition number from simulations of different time lengths. The error bar shows the standard deviation of results from 100 simulations of the same time length. With increasing simulation time, the transition number increases, and the results converge to the correct values (blue and red horizontal lines). (c) Standard deviations of and as functions of the average transition number can be fitted by equation with coefficients: : , : . (d) Logarithm of probability converges to a maximal value in the optimization process with initial values of and . (e) Folding and unfolding rates obtained from the probability optimization method are similar to the results in panel (b). (f) Standard deviations of results from the optimization method can also be fitted by equation with coefficients: for and for .