Bayesian Analysis

Combining experimental data and computer simulations, with an application to flyer plate experiments

Jim Gattiker, Dave Higdon, Sallie Keller-McNulty, Michael McKay, Leslie Moore, and Brian Williams

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A flyer plate experiment involves forcing a plane shock wave through stationary test samples of material and measuring the free surface velocity of the target as a function of time. These experiments are conducted to learn about the behavior of materials subjected to high strain rate environments. Computer simulations of flyer plate experiments are conducted with a two-dimensional hydrodynamic code developed under the Advanced Strategic Computing (ASC) program at Los Alamos National Laboratory. This code incorporates physical models that contain parameters having uncertain values. The objectives of the analyses presented in this paper are to assess the sensitivity of free surface velocity to variations in the uncertain inputs, to constrain the values of these inputs to be consistent with experiment, and to predict free surface velocity based on the constrained inputs. We implement a Bayesian approach that combines detailed physics simulations with experimental data for the desired statistical inference (Kennedy and O'Hagan 2001; Higdon, Kennedy, Cavendish, Cafeo and Ryne 2004).

The approach given here allows for:

  • uncertainty regarding model inputs (i.e. calibration);
  • accounting for uncertainty due to limitations on the number of simulations that can be carried out;
  • discrepancy between the simulation code and the actual physical system;
  • and uncertainty in the observation process that yields the actual field data on the true physical system.
The resulting analysis accomplishes the objectives within a unified framework.

Article information

Bayesian Anal., Volume 1, Number 4 (2006), 765-792.

First available in Project Euclid: 22 June 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

calibration computer experiments flyer plate experiments Gaussian process model validation predictability predictive science sensitivity analysis uncertainty quantification


Williams, Brian; Higdon, Dave; Gattiker, Jim; Moore, Leslie; McKay, Michael; Keller-McNulty, Sallie. Combining experimental data and computer simulations, with an application to flyer plate experiments. Bayesian Anal. 1 (2006), no. 4, 765--792. doi:10.1214/06-BA125.

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