Understanding molecular mechanisms requires estimating dynamical statistics such as expected hitting times, reaction rates, and committors. In systems with well-defined metastable states and free energy barriers, these quantities can be estimated using enhanced sampling methods combined with classical rate theories. However, calculating such statistics for more complex processes with rugged landscapes or multiple pathways requires more general numerical methods. I will describe a framework that Erik Thiede, Dmitris Giannakis, Jonathan Weare, and I recently developed for calculating dynamical statistics by approximating the dynamical operators of the system through a Galerkin expansion. The input data can be many short molecular dynamics trajectories, launched from a nonequilibrium distribution of initial points. A specific choice of basis set in the expansion corresponds to a Markov state model. We have compared this choice to a diffusion-map basis. In our numerical experiments, the diffusion-map basis gives results of comparable or better accuracy to Markov state models. The framework also naturally enables the use of delay embedding to account for memory arising from the use of a subset of coordinates to describe the system.