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

TL;DR

dTRAM is a new statistical method that improves analysis of simulation data across multiple thermodynamic states, providing accurate estimates of stationary and kinetic properties without requiring equilibrium sampling.

Contribution

The paper introduces dTRAM, a novel method that generalizes WHAM and MSM estimators for analyzing discretized trajectory data from multiple thermodynamic states.

Findings

dTRAM outperforms WHAM for non-equilibrium data

dTRAM provides accurate stationary and kinetic estimates

dTRAM unifies WHAM and MSM approaches

Abstract

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