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Using Bayes' Theorem for Free Energy Calculations

Rogers, David M.
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1251832030

Abstract Details

2009, PhD, University of Cincinnati, Arts and Sciences : Chemistry.
Statistical mechanics is fundamentally based on calculating the probabilities of molecular-scaleevents. Although Bayes’ theorem has generally been recognized as providing key guiding principals for setup and analysis of statistical experiments [83], classical frequentist models still predominate in the world of computational experimentation. As a starting point for widespread application of Bayesian methods in statistical mechanics, we investigate the central quantity of free energies from this perspective. This dissertation thus reviews the basics of Bayes’ view of probability theory, and the maximum entropy formulation of statistical mechanics before providing examples of its application to several advanced research areas. We first apply Bayes’ theorem to a multinomial counting problem in order to determine inner shell and hard sphere solvation free energy components of Quasi-Chemical Theory [140]. We proceed to consider the general problem of free energy calculations from samples of interaction energy distributions. From there, we turn to spline-based estimation of the potential of mean force[142], and empirical modeling of observed dynamics using integrator matching. The results of this research are expected to advance the state of the art in coarse-graining methods, as they allow a systematic connection from high-resolution (atomic) to low-resolution (coarse) structure and dynamics. In total, our work on these problems constitutes a critical starting point for further application of Bayes’ theorem in all areas of statistical mechanics. It is hoped that the understanding so gained will allow for improvements in comparisons between theory and experiment.
Thomas Beck, PhD (Committee Chair)
Bruce Ault, PhD (Committee Member)
H Brian Halsall, PhD (Committee Member)
George Stan, PhD (Committee Member)
139 p.
Condensation
Bayes; probability; statistical mechanics; free energy

Recommended Citations

Citations

  • Rogers, D. M. (2009). Using Bayes' Theorem for Free Energy Calculations [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1251832030

    APA Style (7th edition)

  • Rogers, David. Using Bayes' Theorem for Free Energy Calculations. 2009. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1251832030.

    MLA Style (8th edition)

  • Rogers, David. "Using Bayes' Theorem for Free Energy Calculations." Doctoral dissertation, University of Cincinnati, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1251832030

    Chicago Manual of Style (17th edition)

ucin1251832030
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© 2009, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.