An efficient sampling technique for Bayesian inference with computationally demanding models

Technometrics

Volumn 44, Issue 4, 2002, Pages 318-327

  Reichert, Peter ^a   Schervish, Mark ^b   Small, Mitchell J ^b  

^a SWISS FEDERAL INSTITUTE OF AQUATIC SCIENCE AND TECHNOLOGY   (Switzerland)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

Bayesian inference; Computationally demanding model; Copula; Low discrepancy sequence; Markov chain Monte Carlo; Numerical technique

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; MARKOV PROCESSES; MATHEMATICAL MODELS; MONTE CARLO METHODS; NUMERICAL METHODS; OPTIMIZATION; PROBABILITY DENSITY FUNCTION; PROBABILITY DISTRIBUTIONS;

BAYESIAN INFERENCE; COMPUTATIONALLY DEMANDING MODEL; COPULA; LOW-DISCREPANCY SEQUENCE;

SAMPLING;

EID: 0036850517     PISSN: 00401706     EISSN: None     Source Type: Journal    
DOI: 10.1198/004017002188618518     Document Type: Article

References (52)

1. Abbasour, K. C., Schulin, R., Schläppi, E., and Flühler, H. (1996), "A Bayesian Approach for Incorporating Uncertainty and Data Worth in Environmental Projects," Environmental Modeling and Assessment, 1, 151-158.
2. Berger, J. O. (1984), "The Robust Bayesian Viewpoint," in Robustness of Bayesian Analyses, ed. J. Kadane., Amsterdam: North-Holland, pp. 63-124.
3. Brand, K. P., and Small, M. J. (1995), "Updating Uncertainty in an Integrated Risk Assessment: Conceptual Framework and Methods," Risk Analysis, 15, 719-731.
4. Bratley, P., and Fox, B. L. (1988), "ALGORITHM 659: Implementing Sobol's Quasi-Random Sequence Generator," ACM Transactions on Mathematical Software, 14, 88-100.
5. Chaloner, K. M. (1996), "The Elicitation of Prior Distributions," in Bayesian Biostatistics, eds. D. A. Barry and D. K. Stangl, New York, Marcel Dekker, pp. 141-156.
6. Clemen, R. T., and Reilly, T. (1999), "Correlations and Copulas for Decision and Risk Analysis," Management Science, 45, 208-224.
7. Dakins, M. E., Toll, J. E., Small, M. J., and Brand, K. P. (1996), "Risk-Based Environmental Remediation: Bayesian Monte Carlo Analysis and the Expected Value of Sample Information," Risk Analysis, 16, 67-79.
8. Dennis, B. (1996), "Discussion: Should Ecologists Become Bayesians?," Ecological Applications, 6, 1095-1103.
9. Dilks, D. W., Canale, R. P., and Meier, P. G. (1992), "Development of Bayesian Monte Carlo Techniques for Water Quality Model Uncertainty," Ecological Modelling, 62, 149-162.
10. Ellison, A. M. (1996), "An introduction to Bayesian Inference for Ecological Research and Environmental Decision-Making," Ecological Applications, 6, 1036-1046.
11. Fang, K.-T., Wang, Y., and Bentler, P. M. (1994), "Some Applications of Number-Theoretic Methods in Statistics," Statistical Science, 9, 416-428.
12. Finkel, A. M., and Evans, J. S. (1987), "Evaluating the Benefits of Uncertainty Reduction in Environmental Health Risk Management," Journal Air Pollution Control Association, 37, 1164-1172.
13. Freeze, R. A., Massmann, J., Smith, L., Sperling, T., and James, B. (1990), "Hydrogeological Decision Analysis: 1. A Framework," Ground Water, 28, 738-766.
14. Gamerman, D. (1997), Markov Chain Monte Carlo-Statistical Simulation for Bayesian Inference, London: Chapman and Hall.
15. Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (1995), Bayesian Data Analysis, London: Chapman and Hall.
16. Gujer, W., Henze, M., Mino, T., Matsuo, T., Wentzel, M. C., and Marais, G. v. R. (1995), "The Activated Sludge Model No. 2: Biological Phosphorus Removal," Water Science and Technology, 31, 1-11.
17. Gujer, W., Henze, M., Mino, T., and van Loosdrecht, M. (1999), "Activated Sludge Model No. 3," Water Science and Technology, 39, 183-193.
18. Halton, J. H. (1960), "On the Efficiency of Certain Quasi-Random Sequences of Points in Evaluating Multi-Dimensional Integrals," Numerische Mathematik, 2, 84-90.
19. Hammersley, J. M., (1960), "Monte Carlo Methods for Solving Multivariate Problems," Annals of the New York Academy of Science, 86, 844-874.
20. Hammersley, J. M., and Handscomb, D. C. (1964), Monte Carlo Methods, London: Spottiswoode, Ballantyne & Co.
21. Henze, M., Grady, C. P. L., Gujer, W., Marais, G. v. R., and Matsuo, T. (1986), "Activated Sludge Model No. 1," Scientific and Technical Report 1, IAW-PRC Task Group on Mathematical Modelling for Design and Operation of Biological Wastewater Treatment Processes.
22. Hornberger, G. M., and Spear, R. C. (1981), "An Approach to the Preliminary Analysis of Environmental Systems," Journal of Environmental Management, 12, 7-18.
23. Hua, L. K., and Wang, Y. (1981), Applications of Number Theory to Numerical Analysis, Berlin: Springer.
24. Ihaka, R., and Gentleman, R. (1996), "R: A Language for Data Analysis and Graphics," Journal of Computational and Graphical Statistics, 5, 299-314.
25. Iman, R. L., and Conover, W. J. (1982), "A Distribution-Free Approach to Inducing Rank Correlation Among Input Variables," Communication in Statistics-Simulation and Computation, 11, 311-334.
26. Johnson, V. E. (1995), "A Technique for Estimating Marginal Posterior Densities in Hierarchical Models Using Mixtures of Conditional Densities," Journal of the American Statistical Association, 87, 852-860.
27. Kadane, J. B., and Wolfson, L. J. (1998), "Experiences in Elicitation" (with discussion), Journal of the Royal Statistical Society, Ser. D 47, 3-19.
28. Kalagnanam, J. R., and Diwekar, U. M. (1997), "An Efficient Sampling Technique for Off-Line quality control," Technometrics, 39, 308-319.
29. Kruskal, W. H. (1958), "Ordinal Measures of Association," Journal of the American Statistical Association, 53, 814-861.
30. McKay, M. D., Beckman, R. J., and Conover, W. J. (1979), "A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code," Technometrics, 21, 239-245.
31. Nelson R. (1995), "Copulas, Characterization, Correlation, and Counterexamples," Mathematics Magazine, 68, 193-198.
32. Niederreiter, H. (1978), "Quasi-Monte Carlo Methods and Pseudo-Random Numbers," Bulletin of the American Mathematical Society, 84, 957-1041.
33. ____ (1992), Random Number Generation and Quasi-Monte Carlo Methods, Philadelphia: Society for Industrial and Applied Mathematics.
34. Omlin, M., and Reichert, P. (1999), "A Comparison of Model Extrapolation Uncertainty Estimation Techniques," Ecological Modelling, 115, 45-59.
35. Omlin, M., Reichert, P., and Forster, R. (2001), "Biogeochemical Model of Lake Zürich: Model Equations and Results," Ecological Modelling, 141, 77-103.
36. Patwardhan, A., and Small, M. J. (1992), "Bayesian Methods for Model Uncertainty With Application to Future Sea Level Rise," Risk Analysis, 12, 513-523.
37. Ranyard, D., and Smith, J. Q. (1997), "Building a Bayesian Model in a Scientific Environment: Managing Uncertainty After an Accident," in The Practice of Bayesian Analysis, eds. S. French and J. Q. Smith, London: Arnold, pp. 245-258.
38. Reichert, P. (1994), "AQUASIM-A Tool for Simulation and Data Analysis of Aquatic Systems," Water Science and Technology, 30, 21-30.
39. ____ (1995), "Design Techniques of a Computer Program for the Identification of Processes and the Simulation of Water Quality in Aquatic Systems," Environmental Software, 10, 199-210.
40. ____ (2002), "UNCSIM-A Program Package for Uncertainty Analysis and Bayesian Inference," In preparation.
41. Reichert, P., Borchardt, D., Henze, M., Rauch, W., Shanahan, P., Somlyódy, L., and Vanrolleghem, P. (2001), "River Water Quality Model No. 1 (RWQM1): II. Biochemical Process Equations," Water Science and Technology, 43, 11-30.
42. Reichert, P., and Omlin, M. (1997), "On the Usefulness of Overparameterized Ecological models," Ecological Modelling, 95, 289-299.
43. Schweizer, B. (1991), "Thirty Years of Copulas," in Advances of Probability Distributions With Given Marginals, eds. G. Dall' Aglio, S. Kotz, and G. Salinetti, Dordrecht: Kluwer Academic Publishers.
44. Shaw, J. E. H. (1988), "A Quasi-random Approach to Integration in Bayesian Statistics," The Annals of Statistics, 16, 895-914.
45. Small, M. J. and Fischbeck, P. F. (1999), "False Precision in Bayesian Updating With Incomplete Models," Human and Ecological Risk Assessment, 5, 291-304.
46. Smith, J. Q., and French, S. (1993), "Bayesian Updating of Atmospheric Dispersion Models for Use After an Accidental Release of Radiation," The Statistician, 42, 501-511.
47. Sobol, I. M. (1988), "On the Distribution of Points in a Cube and the Approximate Evaluation of Integrals," USSR Computers and Mathematical Physics, 7, 51-70.
48. Sohn, M. D., Small, M. J., and Pantazidou, M. (2000), "Reducing Uncertainty in Site Characterization Using Bayes Monte Carlo Methods," Journal of Environmental Engineering, 126, 893-902.
49. Steinberg, L. J., Reckhow, K. H., and Wolpert, R. L. (1996), "Bayesian Model for Fate and Transport of PCB in Upper Hudson River," Journal of Environmental Engineering, 122, 341-349.
50. Taylor, A. C. (1993), "Using Objective and Subjective Information to Generate Distributions for Probabilistic Exposure Assessment," Journal of Exposure Analysis and Environmental Epidemiology, 3, 285-298.
51. Wolfson, L. J., Kadane, J. B., and Small, M. J. (1996), "Bayesian Environmental Policy Decisions: Two Case Studies," Ecological Applications, 6, 1056-1066.
52. Wolpert, R. L. (1989), "Eliciting and Combining Subjective Judgments About Uncertainty," International Journal of Technology Asessment in Health Care, 5, 537-557.