Bayesian hierarchical uncertainty quantification by structural equation modeling

International Journal for Numerical Methods in Engineering

Volumn 80, Issue 6-7, 2009, Pages 717-737

  Jiang, Xiaomo ^a   Mahadevan, Sankaran ^a  

^a VANDERBILT UNIVERSITY   (United States)

Author keywords

Bayes network; Bayesian updating; Latent variable; Structural equation modeling; Uncertainty quantification

Indexed keywords

BAYES NETWORK; BAYESIAN UPDATING; LATENT VARIABLE; STRUCTURAL EQUATION MODELING; UNCERTAINTY QUANTIFICATION;

BAYESIAN NETWORKS; EQUIVALENCE CLASSES; FORECASTING; HIERARCHICAL SYSTEMS; INFERENCE ENGINES; MEASUREMENT ERRORS; SET THEORY; UNCERTAINTY ANALYSIS;

KNOWLEDGE BASED SYSTEMS;

EID: 70350426510     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2550     Document Type: Article

References (34)

1. Bae H-R, Grandhi RV, Canfield RA. Uncertainty quantification of structural response using evidence theory. AIAA Journal 2003; 41(10):2062-2068.
2. Devolder B, Glimm J, Grove JW, Kang Y, Lee Y, Pao K, Sharp DH, Ye K. Uncertainty quantification for multiscale simulations. Journal of Fluids Engineering (ASME) 2002; 124(1):129-141.
3. Glimm J, Sharp DH. Prediction and the quantification of uncertainty. Physica D 1996; 133(1-4):152-170.
4. Hanson KM. A framework for assessing uncertainties in simulation predictions. Physica D 1999; 133(1-4): 179-188.
5. Hanson KM, Hemez FM. Uncertainty quantification of simulation codes based on experimental data. Proceedings of 41st AIAA Aerospace Sciences, Reno, Nevada, 6-9 January 2003.
6. Mathelin L, Hussaini MY, Zhang TA, Bataille F. Uncertainty propagation for a turbulent, compressible nozzle flow using stochastic methods. AIAA Journal 2004; 42(8):1169-1176.
7. Millman DR, King PI, Maple RC, Beranx PS, Chiltonk LK. Uncertainty quantification with a B-spline stochastic projection. AIAA Journal 2006; 44(8):1845-1853.
8. Oberkampf WL, Trucano TG, Hirsch Ch. Verification, validation, and predictive capabilities in computational engineering and physics. Technical Report Sand. No. 2003-3769, Sandia National Laboratories, Albuquerque, New Mexico, 2003.
9. Witteveen J, Bijl H. Using polynomial chaos for uncertainty quantification in problems with nonlinearities. Proceedings of AIAA-2006-2066, 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, 14th AIAA/ASME/AHS Adaptive Structures Conference, Newport, Rhode Island, 1-4 May 2006.
10. Kennedy MC, O'Hagan A. Bayesian calibration of computer experiments. Journal of the Royal Statistical Society, Series B (Statistical Methodology) 2001; 63(3):425-464.
11. Higdon D, Kennedy M, Cavendish JC, Cafeo JA, Ryne RD. Combining field data and computer simulations for calibration and prediction. SIAM Journal on Scientific Computing 2005; 26(3):448-466.
12. Marcoulides GA, Schumacker RE. New Developments and Techniques in Structural Equation Modeling. Lawrence Erlbaum Associates: Mahwah, NJ, 2001.
13. Goldberger AS. Structural equation methods in the social sciences. Econometrica 1972; 40(6):979-1001.
14. Bielby WT, Hauser RM. Structural equation models. Annual Review of Sociology 1977; 3:137-161.
15. Bentler PM. Multivariate analysis with latent variables: causal modeling. Annual Review of Psychology 1980; 31(1):419-456.
16. Jöreskog KG, Sörbom D. LISREL 8: Structural Equation Modeling with the SIMPLIS Command Language. Scientific Software International: Lincolnwood, IL, 1999.
17. Lee SY, Zhu HT. Statistical analysis of nonlinear structural equation models with continuous and polytomous data. British Journal of Mathematical and Statistical Psychology 2000; 53(2):209-232.
18. Lee SY, Song XY. Bayesian model comparison of nonlinear structural equation models with missing continuous and ordinal categorical data. British Journal of Mathematical and Statistical Psychology 2004; 57(1):131-150.
19. Legler JM, Ryan LM. Latent variable models for Teratogenesis using multiple binary outcomes. Journal of the American Statistical Association 1997; 92(437):13-20.
20. Sammel MD, Ryan LM, Legler JM. Latent variable models for mixed discrete and continuous outcomes. Journal of the Royal Statistical Society, Series B 1997; 59(3):667-678.
21. Arminger G, Muthén BO. A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the Metropolis-Hastings algorithm. Psychometrika 1998; 63(3):271-300.
22. Ansari A, Jedidi K, Jagpal S. A hierarchical Bayesian methodology for treating heterogeneity in structural equation models. Market Science 2000; 19(4):328-347.
23. Tomarken AJ, Waller NG. Structural equation modeling: strengths, limitations, and misconceptions. Annual Review of Clinical Psychology 2005; 1:31-65.
24. Jiang X, Mahadevan S. Bayesian structural equation modeling method for hierarchical model validation. Reliability Engineering and System Safety 2008. DOI: 10.1016/j.ress.2008.08.008.
25. Jensen FV, Jensen FB. Bayesian Networks and Decision Graphs. Springer: New York, 2001.
26. Gelman A, Rubin DB, Stern HS, Garlin JB. Bayesian Data Analysis (2nd edn). Taylor and Francis, CRC: NY, 2004.
27. Gilks GR, Richardson S, Spiegelhalter DJ. Markov Chain Monte Carlo in Practice. Chapman and Hall/CRC: London, U.K., 1996.
28. Mahadevan S, Rebba R. Validation of reliability computational models using Bayes networks. Reliability Engineering and System Safety 2005; 87(2):223-232.
29. Dowding KJ, Pilch M, Hills RG. Formulation of the thermal problem. Computer Methods in Applied Mechanics and Engineering (special issue) 2008; 197:2385-2389.
30. Spiegelhalter DJ, Thomas A, Best NG. WinBUGS Version 1.4 User Manual. MRC Biostatistics Unit: Cambridge, U.K., 2002.
31. Beck JV, Cole KD, Haji-Sheikh A, Litkouhi B. Heat Conduction Using Green's Functions. Hemisphere Publishing Corporation: London, U.K., 1992.
32. Jiang X, Mahadevan S. Bayesian risk-based decision method for reliability assessment of multivariate model. Journal of Applied Statistics 2008; 35(1):49-65.
33. Stephens MA. EDF Statistics for goodness of fit and some comparisons. Journal of the American Statistical Association 1974; 69(347):730-737.
34. NIST/SEMATECH. E-Handbook of Statistical Methods. National Institute of Standards and Technology, 2005. http://www.itl.nist.gov/div898/handbook.