@Article{daume09graining,
  author =       {Pu Liu and Qiang Shi and Hal {Daum\'e III} and Gregory Voth},
  title =        {A Bayesian Statistics Approach to Multiscale Coarse Graining},
  journal =      {Journal of Chemical Physics},
  year =         {2009},
  volume =       {129},
  number =       {21},
  pages =        {214114},
  month =        {December}
  abstract = {
    Coarse-grained (CG) modeling provides a promising way to
    investigate many important physical and biological phenomena over
    large spatial and temporal scales. The multiscale coarse-graining
    (MS-CG) method has been proven to be a thermodynamically
    consistent way to systematically derive a CG model from atomistic
    force information, as shown in a variety of systems, ranging from
    simple liquids to proteins embedded in lipid bilayers. In the
    present work, Bayes' theorem, an advanced statistical tool widely
    used in signal processing and pattern recognition, is adopted to
    further improve the MS-CG force field obtained from the CG
    modeling. This approach can regularize the linear equation
    resulting from the underlying force-matching methodology,
    therefore substantially improving the quality of the MS-CG force
    field, especially for the regions with limited sampling. Moreover,
    this Bayesian approach can naturally provide an error estimation
    for each force field parameter, from which one can know the extent
    the results can be trusted. The robustness and accuracy of the
    Bayesian MS-CG algorithm is demonstrated for three different
    systems, including simple liquid methanol, polyalanine peptide
    solvated in explicit water, and a much more complicated peptide
    assembly with 32 NNQQNY hexapeptides.
  }
}