Calibration of Computational Models With Categorical Parameters and Correlated Outputs via Bayesian Smoothing Spline ANOVA

Curtis Storlie, William A. Lane, Emily M. Ryan, James R. Gattiker, David M. Higdon

Research output: Contribution to journalArticle

20 Scopus citations


It has become commonplace to use complex computer models to predict outcomes in regions where data do not exist. Typically these models need to be calibrated and validated using some experimental data, which often consists of multiple correlated outcomes. In addition, some of the model parameters may be categorical in nature, such as a pointer variable to alternate models (or submodels) for some of the physics of the system. Here, we present a general approach for calibration in such situations where an emulator of the computationally demanding models and a discrepancy term from the model to reality are represented within a Bayesian smoothing spline (BSS) ANOVA framework. The BSS-ANOVA framework has several advantages over the traditional Gaussian process, including ease of handling categorical inputs and correlated outputs, and improved computational efficiency. Finally, this framework is then applied to the problem that motivated its design; a calibration of a computational fluid dynamics (CFD) model of a bubbling fluidized which is used as an absorber in a CO2 capture system. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)68-82
Number of pages15
JournalJournal of the American Statistical Association
Issue number509
StatePublished - Jan 2 2015
Externally publishedYes



  • Categorical inputs
  • Emulator
  • Inverse problem
  • Model calibration
  • Multiple outputs
  • Uncertainty quantification

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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