Python implementation of the multistate Bennett acceptance ratio (MBAR)
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Python implementation of the multistate Bennett acceptance ratio (MBAR) method for estimating expectations and free energy differences from equilibrium samples from multiple probability densities. See our docs.


The easiest way to install the pymbar release is via conda:

conda install -c omnia pymbar

You can also install pymbar from the Python package index using pip:

pip install pymbar

The development version can be installed directly from github via pip:

pip install git+


Basic usage involves importing pymbar and constructing an MBAR object from the reduced potential of simulation or experimental data.

Suppose we sample a 1D harmonic oscillator from a few thermodynamic states:

>>> from pymbar import testsystems
>>> [x_n, u_kn, N_k, s_n] = testsystems.HarmonicOscillatorsTestCase().sample()

We have the nsamples sampled oscillator positions x_n (with samples from all states concatenated), reduced potentials in the (nstates,nsamples) matrix u_kn, number of samples per state in the nsamples array N_k, and indices s_n denoting which thermodynamic state each sample was drawn from.

To analyze this data, we first initialize the MBAR object:

>>> mbar = MBAR(u_kn, N_k)

Estimating dimensionless free energy differences between the sampled thermodynamic states and their associated uncertainties (standard errors) simply requires a call to getFreeEnergyDifferences():

>>> (Deltaf_ij, dDeltaf_ij, Theta_ij) = mbar.getFreeEnergyDifferences()

Here, Deltaf_ij[i,j] is the dimensionless free energy difference f_j - f_i, dDeltaf_ij[i,j] is the standard error in this estimate, and Theta_ij a covariance matrix that can be used to propagate error into quantities derived from the free energies.

Expectations and associated uncertainties can easily be estimated for observables A(x) for all states:

>>> A_kn = x_kn # use position of harmonic oscillator as observable
>>> (EA_k, dEA_k) = mbar.computeExpectations(A_kn)

where EA_k[k] is the estimated expectation of the mean oscillator position in thermodynamic state k.

See the docstring help for these individual methods for more information on exact usage; in Python or IPython, you can view the docstrings with help().



  • Please cite the original MBAR paper:

    Shirts MR and Chodera JD. Statistically optimal analysis of samples from multiple equilibrium states. J. Chem. Phys. 129:124105 (2008). DOI

  • Some timeseries algorithms can be found in the following reference:

    Chodera JD, Swope WC, Pitera JW, Seok C, and Dill KA. Use of the weighted histogram analysis method for the analysis of simulated and parallel tempering simulations. J. Chem. Theor. Comput. 3(1):26-41 (2007). DOI

  • The automatic equilibration detection method provided in pymbar.timeseries.detectEquilibration() is described here:

    Chodera JD. A simple method for automated equilibration detection in molecular simulations. J. Chem. Theor. Comput. 12:1799, 2016. DOI


pymbar is free software and is licensed under the MIT license.


We would especially like to thank a large number of people for helping us identify issues and ways to improve pymbar, including Tommy Knotts, David Mobley, Himanshu Paliwal, Zhiqiang Tan, Patrick Varilly, Todd Gingrich, Aaron Keys, Anna Schneider, Adrian Roitberg, Nick Schafer, Thomas Speck, Troy van Voorhis, Gupreet Singh, Jason Wagoner, Gabriel Rocklin, Yannick Spill, Ilya Chorny, Greg Bowman, Vincent Voelz, Peter Kasson, Dave Caplan, Sam Moors, Carl Rogers, Josua Adelman, Javier Palacios, David Chandler, Andrew Jewett, Stefano Martiniani, and Antonia Mey.