A hierarchical method for Bayesian inference of rate parameters from shock tube data: Application to the study of the reaction of hydroxyl with 2-methylfuran

Research output: Contribution to journalArticleScientificpeer-review


  • Daesang Kim
  • Iman El Gharamti

  • Mireille Hantouche
  • Ahmed E. Elwardany
  • Aamir Farooq
  • Fabrizio Bisetti
  • Omar Knio

Research units

  • King Abdullah University of Science and Technology
  • Alexandria University
  • University of Texas at Austin
  • Duke University


We developed a novel two-step hierarchical method for the Bayesian inference of the rate parameters of a target reaction from time-resolved concentration measurements in shock tubes. The method was applied to the calibration of the parameters of the reaction of hydroxyl with 2-methylfuran, which is studied experimentally via absorption measurements of the OH radical's concentration following shock-heating. In the first step of the approach, each shock tube experiment is treated independently to infer the posterior distribution of the rate constant and error hyper-parameter that best explains the OH signal. In the second step, these posterior distributions are sampled to calibrate the parameters appearing in the Arrhenius reaction model for the rate constant. Furthermore, the second step is modified and repeated in order to explore alternative rate constant models and to assess the effect of uncertainties in the reflected shock's temperature. Comparisons of the estimates obtained via the proposed methodology against the common least squares approach are presented. The relative merits of the novel Bayesian framework are highlighted, especially with respect to the opportunity to utilize the posterior distributions of the parameters in future uncertainty quantification studies.


Original languageEnglish
Pages (from-to)55-67
Number of pages13
JournalCombustion and Flame
Publication statusPublished - 1 Oct 2017
MoE publication typeA1 Journal article-refereed

    Research areas

  • Bayesian inference, Chemical kinetics, Rate parameters, Shock tube, Surrogate model, Uncertainty quantification

ID: 14711788