Statistically optimal analysis of samples from multiple equilibrium states. Journal Article uri icon



  • We present a new estimator for computing free energy differences and thermodynamic expectations as well as their uncertainties from samples obtained from multiple equilibrium states via either simulation or experiment. The estimator, which we call the multistate Bennett acceptance ratio estimator (MBAR) because it reduces to the Bennett acceptance ratio estimator (BAR) when only two states are considered, has significant advantages over multiple histogram reweighting methods for combining data from multiple states. It does not require the sampled energy range to be discretized to produce histograms, eliminating bias due to energy binning and significantly reducing the time complexity of computing a solution to the estimating equations in many cases. Additionally, an estimate of the statistical uncertainty is provided for all estimated quantities. In the large sample limit, MBAR is unbiased and has the lowest variance of any known estimator for making use of equilibrium data collected from multiple states. We illustrate this method by producing a highly precise estimate of the potential of mean force for a DNA hairpin system, combining data from multiple optical tweezer measurements under constant force bias.

publication date

  • September 28, 2008

has subject area

has restriction

  • green

Date in CU Experts

  • September 4, 2015 2:15 AM

Full Author List

  • Shirts MR; Chodera JD

author count

  • 2

Other Profiles

Electronic International Standard Serial Number (EISSN)

  • 1089-7690

Additional Document Info

start page

  • 124105


  • 129


  • 12