Advanced search
Publication Cover
Inverse Problems in Science and Engineering Volume 20, 2012 - Issue 5: Selected papers from the 7th International Conference on Inverse Problems in Engineering – ICIPE 2011, 4–6 May 2011, Orlando, FL, USA
Submit an article Journal homepage
279
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

Practical considerations when using sparse grids with Bayesian inference for parameter estimation

A.F. EmeryDepartment of Mechanical Engineering, University of Washington, Seattle, WA 98195-2600, USA
&
K.C. JohnsonDepartment of Mechanical Engineering, University of Washington, Seattle, WA 98195-2600, USA
Pages 591-608 | Received 28 Feb 2012, Accepted 10 Mar 2012, Published online: 01 May 2012

References

  • Press, WH, Flannery, BP, Teukoslky, SA, and Vetterling, WT, 1986. Numerical Recipes. Cambridge: Cambridge University Press; 1986.
  • Seber, GAF, and Wild, CJ, 1989. Nonlinear Regression. New York: Wiley & Sons; 1989.
  • Shiavi, R, 1999. Introduction To Applied Statistical Signal Analysis. New York: Academic Press; 1999.
  • Bolstad, WM, 2004. Introduction to Bayesian Statistics. New York: Wiley & Sons; 2004.
  • O'Hagan, A, and Forster, J, 2004. Bayesian Inference, Kendall's Advanced Theory of Statistics. Vol. 2b. Oxford: Oxford University Press; 2004.
  • Gelman, A, Carlin, JB, Stern, HS, and Rubin, DB, 2004. Bayesian Data Analysis. Boca Raton, FL: Chapman & Hall/CRC Press; 2004.
  • Carslaw, HS, and Jaeger, C, 1959. Conduction of Heat in Solids. Oxford: Clarendon Press; 1959.
  • COMSOL, Version 3.5a, Heat transfer module user's guide, COMSOL Multiphysics, 2008.
  • Smolyak, S, 1963. Quadrature and interpolation formulas for tenser product of certain classes of functions, Sov. Math. Dokl. 4 (1963), pp. 240–243.
  • Barthelmann, V, Novak, E, and Ritter, K, 2000. High dimensional polynomial interpolation on sparse grids, Adv. Comput. Math. 12 (2000), pp. 273–287.
  • Klimke, A, , 2008. Sparse grid interpolation toolbox user's guide; available at www.ians.uni-stuttgart.de/spinterp/download.htm.
  • MATLAB version 7.1.0., The Mathworks Inc., Natick, MA.
  • Petras, K, 2001. Fast calculation of coefficients in the Smolyak algorithm, Numer. Algor. 26 (2001), pp. 93–109.
  • Heiss, F, and Winschel, V, 2008. Likelihood approximation by numerical integration on sparse grids, J. Econ. 144 (2008), pp. 62–80.
  • Achatz, S, 2003. Higher order sparse grid methods for elliptic partial differential equations with variable coefficients, Computing 71 (2003), pp. 1–15.
  • Garcke, J, and Hegland, M, 2009. Fitting multidimensional data using gradient penalties and the sparse grid combination technique, Computing 84 (2009), pp. 1–25.
  • Gerstner, T, and Griebel, M, 2008. Sparse Grids: Encyclopedia of Quantitative Finance. New York: Wiley & Sons; 2008.
  • Ma, X, and Zabaras, N, 2009. An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations, J. Comput. Phys. 228 (2009), pp. 3084–3112.
  • Ganapathysubramanian, B, and Zabars, N, 2007. Sparse grid collocation schemes for stochastic natural convection problems, J. Comput. Phys. 225 (2007), pp. 652–685.
  • Lin, B, and Tartakovsky, AM, 2009. An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media, Adv. Water Resources 32 (2009), pp. 712–722.
  • Agarwal, N, and Aluru, NR, 2009. Stochastic analysis of electrostatic MEMS subjected to parameter variations, J. Microelectromech. Syst. 18 (2009), pp. 1454–1468.
  • Steffensen, JF, 1950. Interpolation. New York: Chelsea; 1950.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.