Bayesian structural equation modeling method for hierarchical model validation

Reliability Engineering and System Safety

Volumn 94, Issue 4, 2009, Pages 796-809

  Jiang, Xiaomo ^a   Mahadevan, Sankaran ^a  

^a VANDERBILT UNIVERSITY   (United States)

Author keywords

Bayes network; Bayesian statistics; Hypothesis testing; Model validation; Structural equation modeling

Indexed keywords

BAYESIAN NETWORKS; HIERARCHICAL SYSTEMS; INFERENCE ENGINES; KNOWLEDGE BASED SYSTEMS; MARKOV PROCESSES; MONTE CARLO METHODS; SECURITY OF DATA; STATISTICAL TESTS; TIME SERIES;

BAYES NETWORK; BAYESIAN STATISTICS; HYPOTHESIS TESTING; MODEL VALIDATION; STRUCTURAL EQUATION MODELING;

MATHEMATICAL MODELS;

EID: 58749111814     PISSN: 09518320     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ress.2008.08.008     Document Type: Article

References (45)

1. Hasselman TK, Wathugala GW, Crawford J. A hierarchical approach for model validation and uncertainty quantification. In: Mang HA, Rammerstorfer FG, Eberhardsteiner J, editors. Proceeding of the fifth world congress on computational mechanics, Vienna, Austria, July 7-12, 2002.
2. DOD. Verification, validation, and accreditation (VV&A) recommended practices guide (1996), Department of Defense, Alexandria, VA. 〈http://vva.dmso.mil/〉
3. AIAA. Guide for the verification and validation of computational fluid dynamics simulations (1998), American Institute of Aeronautics and Astronautics AIAA-G-077-1998, Reston, VA
4. DOE. Accelerated Strategic Computing Initiative (ASCI) program plan (2000), Department of Energy DOE/DP-99-000010592, Washington, DC
5. ASME. Guide for verification and validation in computational solid mechanics. ASME V&V 10-2006, American Society of Mechanical Engineers.
6. Balci, O. Verification, validation, and accreditation of simulation models. In: Proceedings of the 29th conference on winter simulation, Atlanta, GA, 1997.
7. Roache P.J. Verification and validation in computational science and engineering (1998), Hermosa Publishers, Albuquerque, NM
8. Trucano T.G., Easterling R.G., Dowding K.J., Paez T.L., Urbina A., Romero V.J., et al. Description of the Sandia validation metrics project.Technical report of Sandia no. 2001-1339 (2001), Sandia National Laboratories, Albuquerque, NM
9. Hills R.G., and Trucano T.G. Statistical validation of engineering and scientific models: a maximum likelihood based metric. Technical report of Sandia no. 2001-1783 (2002), Sandia National Laboratories, Albuquerque, NM
10. Oberkampf W.L., and Trucano T.G. Verification and validation in computational fluid dynamics. Prog Aerospace Sci 38 3 (2002) 209-272
11. Paez TL, Urbina A. Validation of mathematical models of complex structural dynamic systems. In: Proceedings of the ninth international congress on sound and vibration, Orlando, FL, 2002.
12. Hills R.G., and Leslie I. Statistical validation of engineering and scientific models: validation experiments to application. Technical report of Sandia no. 2003-0706 (2003), Sandia National Laboratories, Albuquerque, NM
13. Oberkampf W.L., Trucano T.G., and Hirsch Ch. Verification, validation, and predictive capabilities in computational engineering and physics. Technical report of Sandia no. 2003-3769 (2003), Sandia National Laboratories, Albuquerque, NM
14. Babuska I., and Oden J.T. Verification and validation in computational engineering and science: basic concepts. Comput Methods Appl Mech Eng 193 36-38 (2004) 4057-4066
15. Dowding K.J., Hills R.G., Leslie I., Pilch M., Rutherford B.M., and Hobbs M.L. Case study for model validation: assessing a model for thermal decomposition of polyurethane foam. Technical report of Sandia no. 2004-3632 (2004), Sandia National Laboratories, Albuquerque, NM
16. Campbell, K. A brief survey of statistical model calibration ideas. In: International conference on sensitivity analysis of model output, Santa Fe, NM, 2004.
17. Sargent, P. Validation and verification of simulation models. In: Proceedings of the 2004 winter simulation conference, Washington, DC, 2004.
18. Oberkampf W.L., and Trucano T.G. Design of and comparison with verification and validation benchmarks. Technical report of Sandia no. 2006-5376C (2006), Sandia National Laboratories, Albuquerque, NM
19. Oberkampf W.L., and Barone M.F. Measures of agreement between computation and experiment: validation metrics. J Comput Phys 217 1 (2006) 5-36
20. Chen W., Baghdasaryan L., Buranathiti T., and Cao J. Model validation via uncertainty propagation and data transformation. AIAA J 42 7 (2004) 1406-1415
21. Zhang R., and Mahadevan S. Bayesian methodology for reliability model acceptance. Reliab Eng Syst Saf 80 1 (2003) 95-103
22. Mahadevan S., and Rebba R. Validation of reliability computational models using Bayes networks. Reliab Eng Syst Saf 87 2 (2005) 223-232
23. Rebba R., and Mahadevan S. Model predictive capability assessment under uncertainty. AIAA J 44 10 (2006) 2376-2384
24. Jiang X., and Mahadevan S. Bayesian risk-based decision method for model validation under uncertainty. Reliab Eng Syst Saf 92 6 (2007) 707-718
25. Jiang X., and Mahadevan S. Bayesian validation assessment of multivariate computational models. J Appl Stat 35 1 (2008) 49-65
26. Jiang X., and Mahadevan S. Bayesian wavelet method for multivariate model assessment of dynamical systems. J Sound Vib 312 4-5 (2008) 694-712
27. Bollen K.A. Structural equations with latent variables (1989), Wiley, New York
28. Goldberger A.S. Structural equation methods in the social sciences. Econometrica 40 6 (1972) 979-1001
29. Bielby W.T., and Hauser R.M. Structural equation models. Annu Rev Sociol 3 (1977) 137-161
30. Bentler P.M. Multivariate analysis with latent variables: causal modeling. Annu Rev Sociol 31 1 (1980) 419-456
31. Congdon P. Applied Bayesian modelling (2003), Wiley, Chichester
32. Hilborn R., and Mangel M. The ecological detective: confronting models with data (1997), Princeton University Press, Princeton, NJ
33. Martin J.K., and McDonald R.P. Bayesian estimation in unrestricted factor analysis: a treatment for heywood cases. Psychometrika 40 4 (1975) 505-517
34. Lee S.Y. A Bayesian approach to confirmatory factor analysis. Psychometrika 46 2 (1981) 153-160
35. Arminger G., and Muthén B.O. A Bayesian approach to nonlinear latent variable models using the Gibbs sampler and the Metropolis-Hastings algorithm. Psychometrika 63 3 (1998) 271-300
36. Ansari A., Jedidi K., and Jagpal S. A hierarchical Bayesian methodology for treating heterogeneity in structural equation models. Market Sci 19 (2000) 328-347
37. Lopes H.F., and West M. Bayesian model assessment in factor analysis. Stat Sin 14 1 (2004) 41-67
38. Jensen F.V., and Jensen F.B. Bayesian networks and decision graphs (2001), Springer, New York
39. Gilks G.R., Richardson S., and Spiegelhalter D.J. Markov chain Monte Carlo in practice. Interdisciplinary statistics (1996), Chapman & Hall/CRC, London
40. Spiegelhalter D.J., Thomas A., and Best N.G. WinBUGS version 1.4 user manual (2002), MRC Biostatistics Unit, Cambridge, UK
41. Kass R., and Raftery A. Bayes factors. J Am Stat Assoc 90 430 (1995) 773-795
42. Migon H.S., and Gamerman D. Statistical inference-an integrated approach (1999), Arnold, a Member of the Holder Headline Group, London
43. Rebba R., and Mahadevan S. Computer methods for model reliability assessment. Reliab Eng Syst Saf 93 8 (2008) 1197-1207
44. Stoica P., and Moses R.L. Introduction to spectral analysis (1997), Prentice-Hall, Englewood Cliffs, NJ
45. Red-Horse J.R., and Paez T.L. Sandia National Laboratories validation workshop: structural dynamics application. Comput Methods Appl Mech Eng 197 29-32 (2008) 2578-2584