Commentary: Simulation-Aided Inference in Cosmology

Conference paper
Part of the Lecture Notes in Statistics book series (LNS, volume 902)

Abstract

Higdon’s use of Gaussian Process (GP) emulation to analyze SDSS data using simulated power spectra from N-body simulations supplies a textbook case study of a set of techniques that are likely to become a standard part of the astrostatistics toolbox. The problems addressed by these techniques models based on expensive computer simulations that run on high-performance computing (HPC) platforms, which can only sparsely sample a large-dimensional input parameter space are likely to be of interest to a growing community of computational astrophysicists wishing to compare models to data, as this style of computing becomes “democratized” by the increasing availability of HPC platforms in University research settings. We comment here on the computational challenges of Gaussian Process modeling, the fidelity of model hierarchies, and strategies for the adaptive design of numerical experiments.

Keywords

Entropy Manifold Covariance Abate 

References

  1. 1.
    C. Rasmussen, C. Williams: Gaussian Processes for Machine Learning, (MIT Press, 2006)Google Scholar
  2. 2.
    J. Sacks, W. J. Welch, T. J. Mitchell, H. P. Wynn: Design and analysis of computer experiments. Statistical Science 4 (4), 409–423 (1989)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    M. Kennedy, A. O’Hagan: Bayesian calibration of complex computer models. Journal of the Royal Statistical Society Series B 63, 425–464 (2001)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    T. Santner, B. Williams, W. Notz: The Design and Analysis of Computer Experiments. (Springer, 2003)Google Scholar
  5. 5.
    A. O’Hagan: Bayesian Analysis of Computer Code Outputs: A Tutorial. Reliability Engineering and System Safety 91 (10–11), 1290–1300 (2006)CrossRefGoogle Scholar
  6. 6.
    D. Higdon, M. Kennedy, J. Cavendish, J. Cafeo, R. Ryne: Combining field data and computer simulations for calibration and prediction. SIAM Journal on Scientific Computing 26 (2), 448–466 (2004)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    K. Heitmann, D. Higdon, M. White, S. Habib, B. J. Williams, E. Lawrence, C. Wagner: The Coyote Universe. II. Cosmological Models and Precision Emulation of the Nonlinear Matter Power Spectrum. The Astrophysical Journal 705, 156–174 (2009)Google Scholar
  8. 8.
    M. Gibbs, D. MacKay: Efficient implementation of Gaussian processes. Cavendish Lab., Cambridge, UK, Tech. Rep. (1997)Google Scholar
  9. 9.
    J. Skilling: Bayesian numerical analysis. In: Physics & Probability: Essays in honor of Edwin T. Jaynes, 207–221 (1993)Google Scholar
  10. 10.
    G. Wahba, D. Johnson, F. Gao, J. Gong: Adaptive tuning of numerical weather prediction models: Randomized GCV in three- and four-dimensional data assimilation. Monthly Weather Review 123, 3358–3369 (1995) (also available by anonymous ftp from ftp.stat.wisc.edu in pub/wahba)Google Scholar
  11. 11.
    R. Furrer, M. Genton, D. Nychka: Covariance tapering for interpolation of large spatial datasets. Journal of Computational and Graphical Statistics 15 (3), 502–523 (2006)MathSciNetCrossRefGoogle Scholar
  12. 12.
    M. Kennedy, A. O’Hagan: Predicting the output from a complex computer code when fast approximations are available. Biometrika 87 (1), 1–13 (2000)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    J. Cumming, M. Goldstein: Small Sample Bayesian Designs for Complex High-Dimensional Models Based on Information Gained Using Fast Approximations. Technometrics 51 (4), 377–388 (2009)MathSciNetCrossRefGoogle Scholar
  14. 14.
    P. Qian, C. Wu: Bayesian hierarchical modeling for integrating low-accuracy and high-accuracy experiments. Technometrics 50 (2), 192–204 (2008)MathSciNetCrossRefGoogle Scholar
  15. 15.
    R. Gramacy, H. Lee: Adaptive design and analysis of supercomputer experiments. Technometrics 51 (2), 130–145 (2009)MathSciNetCrossRefGoogle Scholar
  16. 16.
    R. B. Gramacy, H. K. H. Lee, W. Macready: Adaptive exploration of computer experiment parameter spaces. Tech. rep., Bulletin of the International Society for Bayesian Analysis (ISBA) (December 2004)Google Scholar
  17. 17.
    T. Loredo, D. Chernoff: Bayesian adaptive exploration. In: AIP Conference Proceedings, Vol. 707, pp. 330–346 (2004)CrossRefGoogle Scholar
  18. 18.
    C. Graziani, T. J. Loredo, M. Anitescu: Adaptive Design of Computer Experiments and Simulation Fidelity Hierarchies. In preparation (2012)Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Astronomy, Flash Center For Computational PhysicsUniversity of ChicagoChicagoUSA

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