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We propose a discrete transition-based reweighting analysis method (dTRAM)for analyzing configuration-space-discretized simulation trajectories producedat different thermodynamic states (temperatures, Hamiltonians, etc.) dTRAMprovides maximum-likelihood estimates of stationary quantities (probabilities,free energies, expectation values) at any thermodynamic state. In contrast tothe weighted histogram analysis method (WHAM), dTRAM does not require data tobe sampled from global equilibrium, and can thus produce superior estimates forenhanced sampling data such as parallel/simulated tempering, replica exchange,umbrella sampling, or metadynamics. In addition, dTRAM provides optimalestimates of Markov state models (MSMs) from the discretized state-spacetrajectories at all thermodynamic states. Under suitable conditions, these MSMscan be used to calculate kinetic quantities (e.g. rates, timescales). In thelimit of a single thermodynamic state, dTRAM estimates a maximum likelihoodreversible MSM, while in the limit of uncorrelated sampling data, dTRAM isidentical to WHAM. dTRAM is thus a generalization to both estimators.

Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states