Fast Bayesian approach for parameter estimation

International Journal for Numerical Methods in Engineering

Volumn 76, Issue 2, 2008, Pages 230-252

  Jin, Bangti ^a  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Bayesian inference approach; Parameter estimation; Proper orthogonal decomposition; Reduced order modeling; Stochastic collocation method

Indexed keywords

BAYESIAN NETWORKS; FUNCTION EVALUATION; INFERENCE ENGINES; INVERSE PROBLEMS; MARKOV PROCESSES; MATHEMATICAL MODELS; METAL ANALYSIS; QUENCHING; STOCHASTIC MODELS;

BAYESIAN APPROACHES; BAYESIAN INFERENCE APPROACH; BAYESIAN MODELS; BOUNDARY MEASUREMENTS; COMPUTATIONAL COSTS; COMPUTATIONAL GAINS; LINEAR INVERSE PROBLEMS; MARKOV CHAINS; MODEL REDUCTION TECHNIQUES; MONTE CARLO; NOISE LEVELS; NON-DESTRUCTIVE EVALUATIONS; NUMERICAL RESULTS; OPTIMAL PROBLEMS; PARAMETERIZED; POSTE-RIORS; PROBLEM SIZES; PROPER ORTHOGONAL DECOMPOSITION; QUENCHING PROCESSES; REDUCED-ORDER MODELING; REGULARIZATION PARAMETERS; ROBIN COEFFICIENTS; SIGNIFICANT REDUCTIONS; STATE SPACES; STOCHASTIC COLLOCATION METHOD; SURROGATE MODELS; TO EFFECTS; UNCERTAINTY PROPAGATIONS;

PARAMETER ESTIMATION;

EID: 57849169391     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2319     Document Type: Article

References (38)

1. Sun NZ, Yeh WG. A stochastic inverse solution for transient groundwater flow: parameter identification and reliability analysis. Water Resources Research 1992; 28(12):3269-3280.
2. Fadale TD, Nenarokomov AV, Emery AF. Uncertainties in parameter estimation: the inverse problem. International Journal of Heat and Mass Transfer 1995; 38(3):511-518.
3. Narayanan VAB, Zabaras N. Stochastic inverse heat conduction using a spectral approach. International Journal for Numerical Methods in Engineering 2004; 60(9):1569-1593.
4. Kaipio J, Somersalo E. Statistical and Computational Inverse Problems. Springer: New York, 2005.
5. Geman S, Geman D. Stochastic relaxation, Gibbs distributions, and Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence 1984; 6(6):721-741.
6. Wang J, Zabaras N. A Bayesian inference approach to the inverse heat conduction problem. International Journal of Heat and Mass Transfer 2004; 47(17-18):3927-3941.
7. Wang J, Zabaras N. Hierarchical Bayesian models for inverse problems in heat conduction. Inverse Problems 2005; 21(1):183-206.
8. Wang J, Zabaras N. Using Bayesian statistics in the estimation of heat source in radiation. International Journal of Heat and Mass Transfer 2005; 48(1):15-29.
9. Emery AF, Valenti E, Bardot D. Using Bayesian inference for parameter estimation when the system response and experimental conditions are measured with error and some variables are considered as nuisance variables. Measurement Science and Technology 2007; 18(1):19-29.
10. Jin B, Zou J. A Bayesian inference approach to the ill-posed Cauchy problem of steady-state heat conduction. International Journal for Numerical Methods in Engineering, submitted.
11. Malinverno A, Briggs VA. Expanded uncertainty quantification in inverse problems: hierarchical Bayes and empirical Bayes. Geophysics 2004; 69(4):1005-1016.
12. Wu H. Statistical methods for HIV dynamic studies in AIDS clinical trials. Statistical Methods in Medical Research 2005; 14(2):171-192.
13. Besag J, Green P, Higdon D, Mengersen K. Bayesian computation and stochastic systems (with Discussions). Statistical Science 1995; 10(1):3-66.
14. Gilks WR, Richardson S, Spiegelhalter DJ (eds). Markov Chain Monte Carlo in Practice. Chapman & Hall: London, 1996.
15. Gelman A, Carlin JB, Stern HS, Rubin DB. Bayesian Data Analysis (2nd edn). Chapman & Hall: Boca Raton, 2003.
16. Fox C, Nicholls G. Statistical estimation of the parameters of a PDE. Canadian Applied Mathematics Quarterly 2002; 10(2):277-306.
17. Higdon D, Lee H, Bi Z. A Bayesian approach to characterizing uncertainty in inverse problems using coarse and fine-scale information. IEEE Transactions on Signal Processing 2002; 50(20):389-399.
18. Balakrishnan S, Roy A, Ierapetritou MG, Flach GP, Georgopoulos PG. Uncertain reduction and characterization for complex environmental fate and transport models: an empirical Bayesian framework incorporating the stochastic response surface method. Water Resources Research 2003; 39(12):1350.
19. Christen JA, Fox C. MCMC using an approximation. Journal of Computational and Graphical Statistics 2005; 14(4):795-810.
20. Marzouk YM, Najm HN, Rahn LA. Stochastic spectral method for efficient Bayesian solution of inverse problems. Journal of Computational Physics 2007; 224(2):560-586.
21. Isukapalli SS, Roy A, Georgopoulos P. Stochastic response surface methods (SRSMs) for uncertainty propagation: application to environmental and biological systems. Risk Analysis 1998; 18(3):351-363.
22. Ghanem R, Spanos P. Stochastic Finite Elements: A Spectral Approach. Springer: New York, 1991.
23. Park HM, Lee MW. Boundary control of the Navier-Stokes equation by empirical reduction of modes. Computer Methods in Applied Mechanics and Engineering 2000; 188(1-3):165-186.
24. Banks HT, Joyner ML, Wincheski B, Winfree WP. Nondestructive evaluation using a reduced-order computational methodology. Inverse Problems 2000; 16(4):929-945.
25. Ostrowski Z, Bialecki RA, Kassab AJ. Estimation of constant thermal conductivity by use of proper orthogonal decomposition. Computational Mechanics 2005; 37(1):52-59.
26. Golub GH, Van Loan CF. Matrix Computations (3rd edn). John Hopkins University Press: Baltimore, MD, 1996.
27. Barrault M, Maday Y, Nguyen NC, Patera AT. An 'empirical interpolation' method: application to efficient reduced-basis discretization of partial differential equations. Comptes Rendus Mathématique 2004; 339(1): 667-672.
28. Xiu D, Hesthaven JS. High-order collocation methods for differential equations with random inputs. SIAM Journal on Scientific Computing 2005; 27(3):1118-1139.
29. Barthelmann V, Novak E, Ritter K. High dimensional polynomial interpolation on sparse grids. Advances in Computational Mathematics 2000; 12(4):273-288.
30. White FM. Heat and Mass Transfer. Addison-Wesley: Reading, MA, 1988.
31. Osman AM, Beck JV. Nonlinear inverse problem for the estimation of time-and-space dependent heat transfer coefficients. Journal of Thermophysics and Heat Transfer 1989; 3(2):146-152.
32. Kaup PG, Santosa F. Nondestructive evaluation of corrosion damage using electrostatic measurements. Journal of Nondestructive Evaluation 1995; 14(3):127-136.
33. Fang W, Cumberbatch E. Inverse problems for metal oxide semiconductor field-effect transistor contact resistivity. SIAM Journal on Applied Mathematics 1992; 52(3):699-709.
34. Jin B. Conjugate gradient method for the Robin inverse problem associated with the Laplace equation. International Journal for Numerical Methods in Engineering 2007; 71(4):433-453.
35. Sincich E. Lipschitz stability for the inverse Robin problem. Inverse Problems 2007; 23(3):1311-1326.
36. Berrut JP, Trefethen LN. Barycentric Lagrange interpolation. SIAM Review 2004; 46(3):501-517.
37. Hanson KM, Cunningham GS. Posterior sampling with improved efficiency. In Medical Imaging: Image Processing, Hanson KM (ed.), Proceedings of SPIE, vol. 3338, San Diego, 1998; 371-382.
38. Gentle JE. Elements of Computational Statistics. Springer: New York, 2002.