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Volumn 224, Issue 2, 2007, Pages 560-586

Stochastic spectral methods for efficient Bayesian solution of inverse problems

Author keywords

Bayesian inference; Diffusive transport; Galerkin projection; Inverse problems; Markov chain Monte Carlo; Monte Carlo; Polynomial chaos; Spectral methods

Indexed keywords

BARIUM COMPOUNDS; BAYESIAN NETWORKS; DIFFERENTIAL EQUATIONS; INFERENCE ENGINES; MARKOV PROCESSES; MONTE CARLO METHODS; POLYNOMIALS; RANDOM VARIABLES; STOCHASTIC SYSTEMS;

EID: 34248523110     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2006.10.010     Document Type: Article
Times cited : (452)

References (64)
  • 3
    • 85190570640 scopus 로고    scopus 로고
    • A. Mohammad-Djafari, Bayesian inference for inverse problems, in: Bayesian inference and Maximum Entropy Methods in Science and Engineering, vol. 21, 2002, pp. 477-496.
  • 4
    • 85190571093 scopus 로고    scopus 로고
    • A. Tarantola, Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, 2005.
  • 6
    • 0000515915 scopus 로고    scopus 로고
    • Resolution of seismic waveform inversion: Bayes versus Occam
    • Gouveia W.P., and Scales J.A. Resolution of seismic waveform inversion: Bayes versus Occam. Inverse Problems 13 (1997) 323-349
    • (1997) Inverse Problems , vol.13 , pp. 323-349
    • Gouveia, W.P.1    Scales, J.A.2
  • 7
    • 0036899002 scopus 로고    scopus 로고
    • Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem
    • Malinverno A. Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem. Geophysical Journal International 151 (2002) 675-688
    • (2002) Geophysical Journal International , vol.151 , pp. 675-688
    • Malinverno, A.1
  • 8
    • 4043130798 scopus 로고    scopus 로고
    • An efficient stochastic Bayesian approach to optimal parameter and uncertainty estimation for climate model predictions
    • Jackson C., Sen M.K., and Stoffa P.L. An efficient stochastic Bayesian approach to optimal parameter and uncertainty estimation for climate model predictions. Journal of Climate 17 (2004) 2828-2841
    • (2004) Journal of Climate , vol.17 , pp. 2828-2841
    • Jackson, C.1    Sen, M.K.2    Stoffa, P.L.3
  • 9
    • 13744250201 scopus 로고    scopus 로고
    • Hierarchical Bayesian models for inverse problems in heat conduction
    • Wang J., and Zabaras N. Hierarchical Bayesian models for inverse problems in heat conduction. Inverse Problems 21 (2005) 183-206
    • (2005) Inverse Problems , vol.21 , pp. 183-206
    • Wang, J.1    Zabaras, N.2
  • 10
    • 9244244173 scopus 로고    scopus 로고
    • Using Bayesian statistics in the estimation of heat source in radiation
    • Wang J., and Zabaras N. Using Bayesian statistics in the estimation of heat source in radiation. International Journal of Heat and Mass Transfer 48 (2005) 15-29
    • (2005) International Journal of Heat and Mass Transfer , vol.48 , pp. 15-29
    • Wang, J.1    Zabaras, N.2
  • 11
    • 85190569157 scopus 로고    scopus 로고
    • T. Loredo, Computational technology for Bayesian inference, in: D.M.R. Plante, D. Roberts (Eds.), ASP Conf. Ser., Astronomical Data Analysis Software and Systems VIII, vol. 172, 1999.
  • 12
    • 0036608343 scopus 로고    scopus 로고
    • Monte Carlo analysis of inverse problems
    • Mosegaard K., and Sambridge M. Monte Carlo analysis of inverse problems. Inverse Problems 18 (2002) R29-R54
    • (2002) Inverse Problems , vol.18
    • Mosegaard, K.1    Sambridge, M.2
  • 13
    • 84972543992 scopus 로고
    • Methods for approximating integrals in statistics with special emphasis on Bayesian integration problems
    • Evans M., and Swartz T. Methods for approximating integrals in statistics with special emphasis on Bayesian integration problems. Statistical Science 10 3 (1995) 254-272
    • (1995) Statistical Science , vol.10 , Issue.3 , pp. 254-272
    • Evans, M.1    Swartz, T.2
  • 14
    • 27144544516 scopus 로고    scopus 로고
    • The role of embedded integration rules in Bayesian statistics
    • Cools R., and Dellaportas P. The role of embedded integration rules in Bayesian statistics. Statistics and Computing 6 (1996) 245-250
    • (1996) Statistics and Computing , vol.6 , pp. 245-250
    • Cools, R.1    Dellaportas, P.2
  • 15
    • 0000576595 scopus 로고
    • Markov chains for exploring posterior distributions
    • Tierney L. Markov chains for exploring posterior distributions. The Annals of Statistics 22 4 (1994) 1701-1728
    • (1994) The Annals of Statistics , vol.22 , Issue.4 , pp. 1701-1728
    • Tierney, L.1
  • 17
    • 0003860037 scopus 로고    scopus 로고
    • Gilks W.R., Richardson S., and Spiegelhalter D.J. (Eds), Chapman & Hall
    • In: Gilks W.R., Richardson S., and Spiegelhalter D.J. (Eds). Markov Chain Monte Carlo in Practice (1996), Chapman & Hall
    • (1996) Markov Chain Monte Carlo in Practice
  • 18
    • 16244389030 scopus 로고    scopus 로고
    • Markov chain Monte Carlo-based approaches for inference in computationally intensive inverse problems
    • Higdon D., Lee H., and Holloman C. Markov chain Monte Carlo-based approaches for inference in computationally intensive inverse problems. Bayesian Statistics 7 (2003) 181-197
    • (2003) Bayesian Statistics , vol.7 , pp. 181-197
    • Higdon, D.1    Lee, H.2    Holloman, C.3
  • 23
    • 0001203226 scopus 로고
    • Hermite expansions in Monte Carlo computation
    • Chorin A. Hermite expansions in Monte Carlo computation. Journal of Computational Physics 8 (1971) 472-482
    • (1971) Journal of Computational Physics , vol.8 , pp. 472-482
    • Chorin, A.1
  • 24
    • 0000531673 scopus 로고
    • Variance reduction in Monte Carlo computations using multi-dimensional Hermite polynomials
    • Maltz F., and Hitzl D. Variance reduction in Monte Carlo computations using multi-dimensional Hermite polynomials. Journal of Computational Physics 32 (1979) 345-376
    • (1979) Journal of Computational Physics , vol.32 , pp. 345-376
    • Maltz, F.1    Hitzl, D.2
  • 25
    • 0000476520 scopus 로고
    • Use of the Wiener-Hermite expansion for nearly normal turbulence
    • Meecham W., and Jeng D. Use of the Wiener-Hermite expansion for nearly normal turbulence. Journal of Fluid Mechanics 32 (1968) 225-249
    • (1968) Journal of Fluid Mechanics , vol.32 , pp. 225-249
    • Meecham, W.1    Jeng, D.2
  • 26
    • 0347659106 scopus 로고
    • Gaussian fields and random flow
    • Chorin A. Gaussian fields and random flow. Journal of Fluid Mechanics 63 (1974) 21-32
    • (1974) Journal of Fluid Mechanics , vol.63 , pp. 21-32
    • Chorin, A.1
  • 27
    • 0000148817 scopus 로고
    • The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals
    • Cameron R., and Martin W. The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals. Annals of Mathematics 48 (1947) 385-392
    • (1947) Annals of Mathematics , vol.48 , pp. 385-392
    • Cameron, R.1    Martin, W.2
  • 30
    • 0033008165 scopus 로고    scopus 로고
    • Stochastic finite elements for heterogeneous media with multiple random non-gaussian properties
    • Ghanem R. Stochastic finite elements for heterogeneous media with multiple random non-gaussian properties. ASCE Journal of Engineering Mechanics 125 (1999) 26-40
    • (1999) ASCE Journal of Engineering Mechanics , vol.125 , pp. 26-40
    • Ghanem, R.1
  • 31
    • 85190569272 scopus 로고    scopus 로고
    • R. Ghanem, J. Red-Horse, A. Sarkar, Modal properties of a space-frame with localized system uncertainties, in: Proceedings of the 8th ASCE Specialty Conference of Probabilistic Mechanics and Structural Reliability, No. PMC200-269, ASCE, 2000.
  • 33
    • 0011074291 scopus 로고    scopus 로고
    • Stochastic modeling of flow-structure interactions using generalized polynomial chaos
    • Xiu D., Lucor D., Su C.-H., and Karniadakis G. Stochastic modeling of flow-structure interactions using generalized polynomial chaos. ASME Journal of Fluids Engineering 124 (2002) 51-59
    • (2002) ASME Journal of Fluids Engineering , vol.124 , pp. 51-59
    • Xiu, D.1    Lucor, D.2    Su, C.-H.3    Karniadakis, G.4
  • 34
    • 0037249229 scopus 로고    scopus 로고
    • The Wiener-Askey polynomial chaos for stochastic differential equations
    • Xiu D., and Karniadakis G. The Wiener-Askey polynomial chaos for stochastic differential equations. SIAM Journal of Scientific Computing 24 2 (2002) 619-644
    • (2002) SIAM Journal of Scientific Computing , vol.24 , Issue.2 , pp. 619-644
    • Xiu, D.1    Karniadakis, G.2
  • 35
    • 0037184252 scopus 로고    scopus 로고
    • Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos
    • Xiu D., and Karniadakis G. Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Computer Methods in Applied Mechanics and Engineering 191 (2002) 4927-4948
    • (2002) Computer Methods in Applied Mechanics and Engineering , vol.191 , pp. 4927-4948
    • Xiu, D.1    Karniadakis, G.2
  • 36
    • 0041782621 scopus 로고    scopus 로고
    • Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation
    • Debusschere B., Najm H., Matta A., Knio O., Ghanem R., and Le Maître O. Protein labeling reactions in electrochemical microchannel flow: Numerical simulation and uncertainty propagation. Physics of Fluids 15 8 (2003) 2238-2250
    • (2003) Physics of Fluids , vol.15 , Issue.8 , pp. 2238-2250
    • Debusschere, B.1    Najm, H.2    Matta, A.3    Knio, O.4    Ghanem, R.5    Le Maître, O.6
  • 37
    • 12044259644 scopus 로고
    • The proper orthogonal decomposition in the analysis of turbulent flows
    • Berkooz G., Holmes P., and Lumley J.L. The proper orthogonal decomposition in the analysis of turbulent flows. Annual Review of Fluid Mechanics 25 (1993) 539-575
    • (1993) Annual Review of Fluid Mechanics , vol.25 , pp. 539-575
    • Berkooz, G.1    Holmes, P.2    Lumley, J.L.3
  • 38
    • 0000246863 scopus 로고
    • Turbulence and the dynamics of coherent structures. Part 1: Coherent structures
    • Sirovich L. Turbulence and the dynamics of coherent structures. Part 1: Coherent structures. Quarterly of Applied Mathematics 45 3 (1987) 561-571
    • (1987) Quarterly of Applied Mathematics , vol.45 , Issue.3 , pp. 561-571
    • Sirovich, L.1
  • 39
    • 1242277349 scopus 로고    scopus 로고
    • Uncertainty reduction and characterization for complex environmental fate and transport models: an empirical Bayesian framework incorporating the stochastic response surface method
    • Balakrishnan S., Roy A., Ierapetritou M.G., Flach G.P., and Georgopoulos P.G. Uncertainty reduction and characterization for complex environmental fate and transport models: an empirical Bayesian framework incorporating the stochastic response surface method. Water Resources Research 39 12 (2003) 1350
    • (2003) Water Resources Research , vol.39 , Issue.12 , pp. 1350
    • Balakrishnan, S.1    Roy, A.2    Ierapetritou, M.G.3    Flach, G.P.4    Georgopoulos, P.G.5
  • 41
    • 85190571659 scopus 로고    scopus 로고
    • C.J. Geyer, Markov chain Monte Carlo maximum likelihood, in: E.M. Keramidas (Ed.), Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, vol. 23, Interface Foundation of North America, 1991, pp. 156-163.
  • 42
    • 0000597408 scopus 로고    scopus 로고
    • Comparison of approximate methods for handling hyperparameters
    • MacKay D.J.C. Comparison of approximate methods for handling hyperparameters. Neural Computation 11 5 (1999) 1035-1068
    • (1999) Neural Computation , vol.11 , Issue.5 , pp. 1035-1068
    • MacKay, D.J.C.1
  • 45
    • 0037299084 scopus 로고    scopus 로고
    • Uncertainty quantification in reacting flow simulations through non-intrusive spectral projection
    • Reagan M., Najm H., Ghanem R., and Knio O. Uncertainty quantification in reacting flow simulations through non-intrusive spectral projection. Combustion and Flame 132 (2003) 545-555
    • (2003) Combustion and Flame , vol.132 , pp. 545-555
    • Reagan, M.1    Najm, H.2    Ghanem, R.3    Knio, O.4
  • 49
    • 0001974429 scopus 로고    scopus 로고
    • Markov chain concepts related to sampling algorithms
    • Gilks W.R., Richardson S., and Spiegelhalter D.J. (Eds), Chapman & Hall
    • Roberts G.O. Markov chain concepts related to sampling algorithms. In: Gilks W.R., Richardson S., and Spiegelhalter D.J. (Eds). Markov Chain Monte Carlo in Practice (1996), Chapman & Hall 45-58
    • (1996) Markov Chain Monte Carlo in Practice , pp. 45-58
    • Roberts, G.O.1
  • 52
    • 3242712896 scopus 로고    scopus 로고
    • Multi-resolution analysis of Wiener-type uncertainty propagation schemes
    • Le Maître O., Najm H., Ghanem R., and Knio O. Multi-resolution analysis of Wiener-type uncertainty propagation schemes. Journal of Computational Physics 197 (2004) 502-531
    • (2004) Journal of Computational Physics , vol.197 , pp. 502-531
    • Le Maître, O.1    Najm, H.2    Ghanem, R.3    Knio, O.4
  • 53
    • 21444449245 scopus 로고    scopus 로고
    • An adaptive multi-element generalized polynomial chaos method for stochastic differential equations
    • Wan X., and Karniadakis G.E. An adaptive multi-element generalized polynomial chaos method for stochastic differential equations. Journal of Computational Physics 209 (2005) 617-642
    • (2005) Journal of Computational Physics , vol.209 , pp. 617-642
    • Wan, X.1    Karniadakis, G.E.2
  • 55
    • 0035452029 scopus 로고    scopus 로고
    • The location of deep salinity sources in the Israeli coastal aquifer
    • Shavit U., and Furman A. The location of deep salinity sources in the Israeli coastal aquifer. Journal of Hydrology 250 (2001) 63-77
    • (2001) Journal of Hydrology , vol.250 , pp. 63-77
    • Shavit, U.1    Furman, A.2
  • 59
    • 0036670764 scopus 로고    scopus 로고
    • Solution of inverse heat conduction problem for determining heat input, weld shape, and grain structure during laser welding
    • Karkhin V.A., Plochikhine V.V., and Bergmann H.W. Solution of inverse heat conduction problem for determining heat input, weld shape, and grain structure during laser welding. Science and Technology of Welding and Joining 7 4 (2002) 224-231
    • (2002) Science and Technology of Welding and Joining , vol.7 , Issue.4 , pp. 224-231
    • Karkhin, V.A.1    Plochikhine, V.V.2    Bergmann, H.W.3
  • 60
    • 2942753787 scopus 로고    scopus 로고
    • A Bayesian inference approach to the inverse heat conduction problem
    • Wang J., and Zabaras N. A Bayesian inference approach to the inverse heat conduction problem. International Journal of Heat and Mass Transfer 47 (2004) 3927-3941
    • (2004) International Journal of Heat and Mass Transfer , vol.47 , pp. 3927-3941
    • Wang, J.1    Zabaras, N.2
  • 62
    • 85190569218 scopus 로고    scopus 로고
    • J.G. Verwer, B.P. Sommeijer, W. Hundsdorfer, RKC time-stepping for advection-diffusion-reaction problems, CWI Report MAS-E0405, CWI, Amsterdam, The Netherlands, 2004.
  • 63
    • 0001789959 scopus 로고    scopus 로고
    • Introduction to general state-space Markov chain theory
    • Gilks W.R., Richardson S., and Spiegelhalter D.J. (Eds), Chapman & Hall
    • Tierney L. Introduction to general state-space Markov chain theory. In: Gilks W.R., Richardson S., and Spiegelhalter D.J. (Eds). Markov Chain Monte Carlo in Practice (1996), Chapman & Hall 59-74
    • (1996) Markov Chain Monte Carlo in Practice , pp. 59-74
    • Tierney, L.1
  • 64
    • 84972511893 scopus 로고
    • Practical Markov chain Monte Carlo
    • Geyer C.J. Practical Markov chain Monte Carlo. Statistical Science 7 4 (1992) 473-483
    • (1992) Statistical Science , vol.7 , Issue.4 , pp. 473-483
    • Geyer, C.J.1


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