Conditionally externally Bayesian pooling operators in chain graphs

Annals of Statistics

Volumn 25, Issue 4, 1997, Pages 1740-1761

  Faria Jr , Álvaro E ^a   Smith, Jim Q ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Bayesian multivariate decision analysis; Chain graphs; Expert systems; External Bayesianity; Logarithmic opinion pools

Indexed keywords

EID: 0031486435     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1031594740     Document Type: Article

References (47)

1. BACHARACH, M. (1972). Scientific disagreement. Christchurch, Oxford. Unpublished manuscript.
2. BACHARACH, M. (1975). Group decisions in the face of differences of opinion. Management Science 22 182-191.
3. BATES, J. M. and GRANGER, C. W. J. (1969). The combination of forecasts. Oper. Res. 20 451-468.
4. BAYARRI, M. J. and DEGROOT, M. H. (1988). Gaining weight: a Bayesian approach. In Bayesian Statistics 3 (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.) 25-44. Oxford Univ. Press.
5. COOKE, R. M. (1991). Experts in Uncertainty: Expert Opinion and Subjective Probability in Science. Oxford Univ. Press.
6. DALKEY, N. C. (1972). An impossibility theorem for group probability functions. Report No. P-4862, The Rand Corporation, Santa Monica, CA.
7. DALKEY, N. C. (1975). Toward a theory of group estimation. In The Delphi Method: Techniques and Applications (H. A. Linstone and M. Turoff, eds.) 236-261. Addison-Wesley, Reading, MA.
8. DAWID, A. P. (1979). Conditional independence in statistical theory (with discussion). J. Roy. Statist. Soc. Ser. B 41 1-31.
9. DAWID, A. P. (1992). Applications of a general propagation algorithm for probabilistic expert systems. Statist. Comput. 2 25-36.
10. DEGROOT, M. H. and MORTERA, J. (1991). Optimal linear opinion pools. Management Science 37 546-558.
11. FARIA, A. E. (1996). Graphical Bayesian models in multivariate expert judgements and conditional external Bayesianity. Ph.D. dissertation, Dept. Statistics, Univ. Warwick.
12. FARIA, A. E. and SMITH, J. Q. (1994). Conditional external Bayesianity in chain graphs. Technical Report 271, Dept. Statistics, Univ. Warwick.
13. FARIA, A. E. and SMITH, J. Q. (1996). Conditional external Bayesianity in decomposable influence diagrams. In Bayesian Statistics 5 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 551-560. Clarendon Press, Oxford.
14. FARIA, A. E. and SOUZA, R. C. (1995). A re-evaluation of the quasi-Bayes approach to the linear combination of forecasts. Journal of Forecasting 14 533-542.
15. FRENCH, S. (1985). Group consensus probability distributions: a critical survey. In Bayesian Statistics 2 (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.) 183-202. North-Holland, Amsterdam.
16. FRYDENBERG, M. (1990). The chain graph Markov property. Scand. J. Statist. 17 333-353.
17. GEANOKOPLOS, J. (1992). Common knowledge. Journal of Economic Perspectives 6 53-82.
18. GENEST, C. (1984). A characterization theorem for externally Bayesian groups. Ann. Statist. 12 1110-1115.
19. GENEST, C., MCCONWAY, K. J. and SCHERVISH, M. J. (1986). Characterization of externally Bayesian pooling operators. Ann. Statist. 14 487-501.
20. GENEST, C. and WAGNER, C. G. (1984). Further evidence against independence preservation in expert judgement synthesis. Technical Report 84-10, Dept. Statistics and Actuarial Science, Univ. Waterloo.
21. GENEST, C. and ZIDEK, J. V. (1986). Combining probability distributions: a critique and an annotated bibliography (with discussion). Statist. Sci. 1 114-148.
22. HEWITT, E. and STROMBERG, K. (1965). Real and Abstract Analysis. Springer, New York.
23. JENSEN, F., JENSEN, F. V. and DITTMER, S. L. (1994). From influence diagrams to junction trees. Report R-94-2013, Dept. Mathematics and Computer Science, Aalborg Univ., Denmark.
24. LADDAGA, R. (1977). Lehrer and the consensus proposal. Synthese 36 473-477.
25. LAURITZEN, S. L. (1996). Graphical Models. Oxford Univ. Press.
26. LAURITZEN, S. L., SPEED, T. P. and VIJAYAN, K. (1984). Decomposable graphs and hypergraphs. J. Austral. Math. Soc. Ser. A 36 12-29.
27. LAURITZEN, S. L. and SPIEGELHALTER, D. J. (1988). Local computations with probabilities on graphical structures and their application to expert systems. J. Roy. Statist. Soc. Ser. B 50 157-224.
28. LEHRER, K. and WAGNER, C. G. (1983). Probability amalgamation and the independence issue: a reply to Laddaga. Synthese 55 339-346.
29. LINDLEY, D. V. (1985). Reconciliation of discrete probability distributions. In Bayesian Statistics 2 (J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith, eds.) 375-390. North-Holland, Amsterdam.
30. MADANSKY, A. (1964). Externally Bayesian groups. Rand Memo RM-4141-PR.
31. MADANSKY, A. (1978). Externally Bayesian groups. Univ. Chicago. Unpublished manuscript.
32. MCCONWAY, K. J. (1978). The combination of experts' opinions in probability assessment: some theoretical considerations. Ph.D. dissertation, Univ. College London.
33. MCCONWAY, K. J. (1981). Marginalization and linear opinion pools. J. Amer. Statist. Assoc. 76 410-414.
34. MENDEL, M. B. and SHERIDAN, T. B. (1987). Optimal estimation using human experts. Manmachine Systems Lab., Dept. Mechanical Engineering, MIT.
35. PEARL, J. (1988). Probabilistic Reasoning in Intelligence Systems. Morgan Kaufmann, San Mateo, CA.
36. PILL, J. (1971). The Delphi method: substance, context, a critique and an annotated bibliography. Socio-Economic Planning and Science 5 57-71.
37. QUEEN, C. M. and SMITH, J. Q. (1993). Multiregression dynamic models. J. Roy. Statist. Soc. Ser. B 55 849-870.
38. RAIFFA, H. (1968). Decision Analysis: Introductory Lectures on Choices under Uncertainty 211-226. Addison-Wesley, Reading, MA.
39. RUDIN, W. (1986). Real and Complex Analysis. McGraw-Hill, New York.
40. SMITH, A. F. M. and MAKOV, U. E. (1978). A quasi-Bayes sequential procedure for mixtures. J. Roy. Statist. Soc. Ser. B 40 106-112.
41. SMITH, J. Q. (1989). Influence diagrams for statistical modelling. Ann. Statist. 17 654-672.
42. SMITH, J. Q. and PAPAMICHAIL, K. N. (1996). Fast Bayes and the dynamic junction forest. Real Time Online Decision Support System document (WG1)-TN(96)-02.
43. STONE, M. (1961). The opinion pool. Ann. Math. Statist. 32 1339-1342.
44. WERMUTH, N. and LAURITZEN, S. L. (1990). On substantive research hypotheses, conditional independence graphs and graphical chain models. J. Roy. Statist. Soc. Ser. B 52 21-50.
45. WEST, M. and HARRISON, P. J. (1989). Bayesian Forecasting and Dynamic Models. Springer, New York.
46. WINKLER, R. L. (1968). The consensus of subjective probability distributions. Management Science 15 B61-B75.
47. WINKLER, R. L. (1986). Expert resolution. Management Science 32 298-303.