Logarithmic pooling of priors linked by a deterministic simulation model

Journal of Computational and Graphical Statistics

Volumn 8, Issue 3, 1999, Pages 452-478

  Givens, Geof H ^a   Roback, Paul J ^b  

^a Department of Environmental and Radiological Health Sciences   (United States)

^b BUCKNELL UNIVERSITY   (United States)

Author keywords

Adaptive importance sampling; Bayesian statistics; Model inversion; Prior coherization

Indexed keywords

EID: 0033245946     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.1999.10474826     Document Type: Article

References (45)

1. Bacharach, M (1979), “Normal Bayesian Dialogues,” Journal of the American Statistical Association, 74, 837-846.
2. Bickel, P. J., and Doksum, K. A. (1977), Mathematical Statistics: Basic Ideas and Selected Topics, San Francisco, CA: Holden-Day.
3. Bogstad, B., Tjelmeland, S., Tjelta, T., and Ulltang, O. (1992), “Description of a Multispecies Model for the Barents Sea (MULTSPEC) and a Study of its Sensitivity to Assumptions on Food Preferences and Stock Sizes of Minke Whales and Haip Seals,” paper SC/44/09 presented to the IWC Scientific Committee, June, 1992.
4. Butterworth, D. S., and Punt, A. E. (1995), “On the Bayesian Synthesis Approach Suggested for the Assessment of the Bering-Chukchi-Beaufort Seas Stock of Bowhead Whales,” Report of the International Whaling Commission, 45, 303-312.
5. Cooke, R. M. (1990), “Statistics in Expert Resolution: A Theory of Weights for Combining Expert Opinion,” in Statistics in Science. The Foundations of Statistical Methods in Biology, Physics, and Economics, eds. R. Cooke and D. Constantini, Netherlands: Kluwer, pp. 41-72.
6. Cox, Jr., L. A. (1991), “Knowledge-Based Resolution of Conflicting Expert Opinions,” Journal of Applied Statistics, 18, 23-34.
7. Cubasch, U., and Cess, R. D. (1990), “Processes and Modelling,” in Climate Change, The IPCC Scientific Assessment, eds. J. J. Ephraums, J. T. Houghton, and G. J. Jenkins, Cambridge: Cambridge University Press.
8. French, S. (1985), “Group Consensus Probability Distributions: A Critical Survey,” in Bayesian Statistics 2, eds. J. M. Bernardo, M. H. DeGroot, D. Lindley, and A. F. M. Smith, Amsterdam: Elsevier, pp. 183-202.
9. Gelman, A., Bois, F., and Jiang, J. (1996), “Physiological Pharmacokinetic Analysis Using Population Modeling and Informative Prior Distributions,” Journal of the American Statistical Association, 91, 1400-1412.
10. Genest, C. (1984), “A Characterization Theorem for Externally Bayesian Groups,” The Annals of Statistics, 12, 1100-1105.
11. Genest, C., Weerahandi, S., and Zidek, J. V. (1984), “Aggregating Opinions Through Logarithmic Pooling,” Theory and Decision, 17, 61-70.
12. Genest, C., and Zidek, J. V. (1986), “Combining Probability Distributions: A Critique and an Annotated Bibliography” (with discussion), Statistical Science, 1, 114-148.
13. Givens, G. H., and Raftery, A. E. (1996), “Local Adaptive Importance Sampling for Multivariate Densities With Strong Nonlinear Relationships,” Journal of the American Statistical Association, 91, 132-141.
14. Givens, G. H., Zeh, J. E., and Raftery, A. E. (1995), “Assessment of the Bering-Chukchi-Beaufort Seas Stock of Bowhead Whales Using the BALEEN II Population Model in a Bayesian Synthesis Framework,” Report of the International Whaling Commission, 45, 345-364.
15. Green, E. J., and Strawderman, W. E. (1996), “A Bayesian Growth and 'Weld Model for Slash Pine Plantations,” Journal of Applied Statistics, 23, 285-299.
16. Hammersley, J. M., and Hanscomb, D. C. (1964), Monte Carlo Methods, London: Methuen.
17. Henderson-Sellers, A., and Robinson, P. J. (1986), Contemporary Climatology, New York: Wiley.
18. Hethcote, H. W., van Ark, J. W., and Karon, J. M. (1991a), “A Simulation Model of AIDS in San Francisco: II. Simulations, Therapy, and Sensitivity Analysis,” Mathematical Biosciences, 106, 223-247.
19. Hethcote, H. W., van Ark, J. W., and Longini, Jr., I. M. (1991b), “A Simulation Model of AIDS in San Francisco: I. Model Formulation and Parameter Estimation,” Mathematical Biosciences, 106, 203-222.
20. Izenman, A. J. (1991), “Recenty Developments in Nonparametric Density Estimation,” Journal of the American Statistical Association, 86, 205-224.
21. Jacobs, R. A. (1995), “Methods for Combining Experts’ Probability Assessments,” Neural Computation, 1, 867-888.
22. Kolmogorov, A. N. (1933), “Sulla Determinazione Empirica di una Legge di Distribuzione,” Giomale dell’ Istituto Italiano degli Attuari, 4, 83-91.
23. Lindley, D. V. (1983), “Reconciliation of Probability Distributions,” Operations Research, 31, 866-880.
24. Lindley, D. V (1985), “Reconciliation of Discrete Probability Distributions,” in Bayesian Statistics 2, eds. J. M. Bernardo, M. H. DeGroot, D. Lindley, and A. F. M. Smith, Amsterdam: Elsevier Science Publishers, pp. 375-390.
25. Madansky, A. (1978), “Externally Bayesian Groups,” unpublished manuscript, University of Chicago.
26. McConway, K. J. (1978), “The Combination of Experts’ Opinions in Probability Assessment: Some Theoretical Considerations,” unpublished PhD thesis, London: University College.
27. Morris, P. A. (1977), “Combining Expert Judgments: A Bayesian Approach,” Management Science, 29, 679-693.
28. Oglesby, R. J., Maasch, K. A., and Saltzman, B. (1989), “Glacial Meltwater Cooling of the Gulf of Mexico: GCM Implications for Holocene and Present-Day Climates,” Climate Dynamics, 3, 115-133.
29. Parzen, E. (1962), “On the Estimation of a Probability Density Function and the Mode,” Annals of Mathematical Statistics, 33, 1065-1076.
30. Poole, D., and Raftery, A. E. (1998), “Assessment of the Bering-Chukchi-Beaufort Seas Stock of Bowhead Whales Using Bayesian and Full Pooling Bayesian Synthesis Methods,” paper SC/50/AS6 presented to the IWC Scientific Committee, May 1998.
31. Raftery, A. E., Givens, G. H., and Zeh, J. E. (1995), “Inference From a Deterministic Population Dynamics Model for Bowhead Whales” (with discussion), Journal of the American Statistical Association, 90, 402-430.
32. Raftery, A. E., and Poole, D. (1997), “Bayesian Synthesis Assessment Methodology for Bowhead Whales,” paper SC/49/AS5 presented to the IWC Scientific Committee, September, 1997.
33. Raftery, A. E., Poole, D., and Givens, G. H. (1996), “The Bayesian Synthesis Assessment Method: Resolving the Borel Paradox and Comparing the Backwards and Forwards Variants,” paper SC/48/AS16 presented to the IWC Scientific Committee, June, 1996.
34. Roback, P. J. (1998), “The Pooling of Prior Distributions via Logarithmic and supra-Bayesian Methods With Application to Bayesian Inference in Deterministic Simulation Models,” unpublished PhD thesis, Colorado State University, Department of Statistics.
35. Rosenblatt, M. (1956), “Remarks on Some Nonparametric Estimates of a Density Function,” Annals of Mathematical Statistics, 27, 832-837.
36. Schweder, T., and Hjort, N. L. (1997), “Indirect and Direct Likelihoods and Their Synthesis-With an Appendix on Minke Whale Dynamics,” paper SC/49/AS9 presented to the IWC Scientific Committee, September 1997.
37. Schweder, T., and Ianelli, J. N. (1998), “Bowhead Assessment by Likelihood Synthesis, Methods and Difficulties,” paper SC/50/AS2 presented to the IWC Scientific Committee, May 1998.
38. Simmons, A. J., and Bengtsson, L. (1984), “Atmospheric General Circulation Models, Their Design and Use for Climate Studies,” in The Global Climate, ed. J. Houghton, Cambridge: Cambridge University Press.
39. Smirnov, N. V. (1939), “Estimate of Deviation Between Empirical Distribution Functions of Two Independent Samples” (in Russian), Bulletin of Moscow University, 2, 3-16.
40. Stone, M. (1961), “The Opinion Pool,” Annals of Mathematical Statistics, 32, 1339-1342.
41. Weerahandi, S., and Zidek, J. V. (1978), “Multi-Bayesian Statistical Decision Theory,” Report No. 78-34, Institute of Applied Mathematics and Statistics, University of British Columbia.
42. Westergaard, H. (1968), Contributions to the History of Statistics, New York: Agathon, p. 22.
43. Winkler, R. L. (1968), “The Consensus of Subjective Probability Distributions,” Management Science, 15, B61-B75.
44. Winkler, R. L. (1981), “Combining Probability Distributions From Dependent Information Sources,” Management Science, 27, 479-488.
45. Wolpert, R. L. (1995), Comment on “Inference From a Deterministic Population Dynamics Model for Bowhead Whales,” Journal of the American Statistical Association, 90, 426-427.