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Direct simulation of biomolecular dynamics in thermal equilibrium ischallenging due to the metastable nature of conformation dynamics and thecomputational cost of molecular dynamics. Biased or enhanced sampling methodsmay improve the convergence of expectation values of equilibrium probabilitiesand expectation values of stationary quantities significantly. Unfortunatelythe convergence of dynamic observables such as correlation functions ortimescales of conformational transitions relies on direct equilibriumsimulations. Markov state models are well suited to describe both, stationaryproperties and properties of slow dynamical processes of a molecular system, interms of a transition matrix for a jump process on a suitable discretiza- tionof continuous conformation space. Here, we introduce statistical estimationmethods that allow a priori knowledge of equilibrium probabilities to beincorporated into the estimation of dynamical observables. Both, maximumlikelihood methods and an improved Monte Carlo sampling method for reversibletransition ma- trices with fixed stationary distribution are given. Thesampling approach is applied to a toy example as well as to simulations of theMR121-GSGS-W peptide, and is demonstrated to converge much more rapidly than aprevious approach in [F. Noe, J. Chem. Phys. 128, 244103 (2008)]

Efficient Bayesian estimation of Markov model transition matrices with given stationary distribution