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MA 797

Uncertainty Quantification for Physical and Biological Models




Books (** Especially Recommended)

  • *** R.C. Smith, Uncertainty Quantification: Theory, Implementation and Applications}, SIAM, Philadelphia, PA 2014.
  • ** D.G. Cacuci, Sensitivity and Uncertainty Analysis, Theory, Chapman and Hall/CRC, 2003.
  • P. Knupp and K. Salari, Verification of Computer Codes in Computational Science and Engineering, Chapman and Hall/CRC, Boca Raton, FL, 2003.
  • ** W.L. Oberkampf and C.J. Roy, Verification and Validation in Scientific Computing}, Cambridge University Press, 2010.
  • P.J. Roache, Verification and Validataion in Computational Science and Engineering, Hermosa Publishers, Albuquerque, NM, 1998.
  • T.J. Santner, B.J. Williams and W.I. Notz, The Design and Analysis of Computer Experiments, Springer, Berlin, 2003.
  • R.C. Smith, Smart Material Systems: Model Development, SIAM, Philadelphia, PA, 2005 (Chapter 7: Rod, Beam, Plate and Shell Models PDF; Chapter 8: Numerical Techniques PDF; Appendix C: Legendre Transforms, Calculus of Variations, and Mechanics Principles PDF; Bibliography PDF).

Tutorial Slides on MATLAB, Linear Algebra and Numerical Analysis

  • "Introduction to MATLAB and Linear Algebra'', PDF
  • "Introduction to Numerical Integration, Optimization, Differentiation and Differential Equations'', PDF

MATLAB-R-Python

  • D. Hiebeler, "MATLAB/R Reference'', PDF
  • "MATLAB-Python-R'', PDF

Papers

  • A. Alexanderian, "A brief note on the Karhunen-Loeve expansion'' PDF.
  • B.M. Adams, H.T. Banks, M. Davidian, H-D. Kwon, H.T. Tran, S.N. Wynne and E.S. Rosenberg, "HIV dynamics: Modeling, data analysis, and optimal treatment protocols,'' Journal of Computational and Applied Mathematics,'' 184, pp. 10-49, 2005 PDF.
  • C. Andrieu and J. Thomas, "A tutorial on adaptive MCMC,'' Statistics and Computing, 18, pp. 343-373, 2008.
  • I. Babuska, F. Nobile and R. Tempone, "Reliability of computational science,'' in Numerical Methods for Partial Differential Equations, 23(4), pp. 753-784, 2007.
  • H.T. Banks, M. Davidian, J.R. Samuels, Jr., and K.L. Sutton, "An inverse problem statistical methodology summary,'' Workshop on Biomedical Modeling and Cardiovascular-Respiratory Control, Schloss Seggau, Leibnitz, Austria, 2007; CRSC Technical Report CRSC-TR08-01 PDF.
  • R.G. Hills and T.G. Trucano, "Statistical validation of engineering and scientific models: Background, Sandia Report SAND99-1256, 1999.
  • W.L. Oberkampf and T.G. Trucano, "Verification and validation in computational fluid dynamics,'' Progress in Aerospace Sciences, 38, pp. 209-272, 2002.
  • W.L. Oberkampf, T.G. Trucano and C. Hirsch, "Verification, validation, and predictive capability in computational engineering and physics,'' Applied Mechanics Review, 57(5), pp. 345-384, 2004.
  • A. O'Hagan, "Bayesian analysis of computer code outputs: A tutorial,'' Reliability Engineering and System Safety, 91, pp. 1290-1300, 2006.
  • M.C. Kennedy and A. O'Hagan, "Bayesian callibration of computer models,'' Journal of the Royal Statistical Society B, 63, pp. 425-464, 2001.
  • C.J. Roy, "Review of code and solution verification procedures for computational simulation,'' Journal of Computational Physics, 205, pp. 131-156, 2005.
  • C.J. Roy and A. Raju, "Estimation of discretization errors using the method of nearby problems,'' AIAA Journal, 45(6), pp. 1232-1243, 2007.
  • R.D. Skeel, "Thirteen ways to estimate global error,'' Numerische Mathematik, 48(1), pp. 1-20, 1986.
  • P.E. Zadunaisky, "On the estimation of errors propogated in the numerical integration of ordinary differential equations,'' Numerische Mathematik, 27, pp. 21-29, 1976.