Re-examining informative prior elicitation through the lens of Markov chain Monte Carlo methods

Journal of the Royal Statistical Society. Series A: Statistics in Society

Volumn 169, Issue 1, 2006, Pages 37-48

  Hahn, Eugene D ^a  

^a SALISBURY UNIVERSITY   (United States)

Author keywords

Bayesian inference; Kullback Leibler divergence; Markov chain Monte Carlo methods; Non conjugate priors; Pentagonal distribution

Indexed keywords

EID: 33645061773     PISSN: 09641998     EISSN: 1467985X     Source Type: Journal    
DOI: 10.1111/j.1467-985X.2005.00381.x     Document Type: Article

References (33)

1. Berger, J. O. (1985) Statistical Decision Theory and Bayesian Analysis. New York: Springer.
2. Berger, J. O. (2000) Bayesian analysis: a look at today and thoughts of tomorrow. J. Am. Statist. Ass., 95, 1269-1276.
3. Carlin, B. P., Kass, R. E., Lerch, F. J. and Huguenard, B. R. (1992) Predicting working memory failure: a subjective Bayesian approach to model selection. J. Am. Statist. Ass., 87, 319-327.
4. Chaloner, K. (1996) Elicitation of prior distributions. In Bayesian Biostatistics (eds D. A. Berry and D. K. Stangl), pp. 141-156. New York: Dekker.
5. Chaloner, K. M. and Duncan, G. T. (1983) Assessment of a beta prior distribution: PM elicitation. Statistician, 32, 174-180.
6. Dalal, S. R. and Hall, W. J. (1983) Approximating priors by mixtures of natural conjugate priors. J. R. Statist. Soc. B, 45, 278-286.
7. Diaconis, P. and Ylvisaker, D. (1985) Quantifying prior opinion. In Bayesian Statistics 2 (eds J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith), pp. 133-156. Amsterdam: North-Holland.
8. Dickey, J. M. and Chen, C.-H. (1985) Direct subjective-probability modelling using ellipsoidal distributions. In Bayesian Statistics 2 (eds J. M. Bernardo, M. H. DeGroot, D. V. Lindley and A. F. M. Smith), pp. 157-182. Amsterdam: North-Holland.
9. van Dorp, J. R. and Kotz, S. (2003) Generalized trapezoidal distributions. Metrika, 58, 85-97.
10. Garthwaite, P. H. and Dickey, J. M. (1988) Quantifying expert opinion in linear regression problems. J. R. Statist. Soc. B, 50, 462-474.
11. Gelfand, A. E., Mallick, B. K. and Dey, D. K. (1995) Modeling expert opinion arising as a partial probabilistic specification. J. Am. Statist. Ass., 90, 598-604.
12. Hogarth, R. M. (1975) Cognitive processes and the assessment of subjective probability distributions. J. Am. Statist. Ass., 70, 271-289.
13. Jaynes, E. T. (1989) Brandeis lectures. In E. T. Jaynes: Papers on Probability, Statistics, and Statistical Physics (ed. R. D. Rosenkrantz), pp. 39-76. Dordrecht: Kluwer.
14. Kadane, J. B., Dickey, J. M., Winkler, R. L., Smith, W. S. and Peters, S. C. (1980) Interactive elicitation of opinion for a normal linear model. J. Am. Statist. Ass., 75, 845-854.
15. Kadane, J. B., Shmueli, G., Minka, T. P., Borle, S. and Boatwright, P. (2005) Conjugate analysis of the Conway-Maxwell-Poisson distribution. Bayes. Anal., to be published.
16. Kass, R. E. and Wasserman, L. (1996) The selection of prior distributions by formal rules. J. Am. Statist. Ass., 91, 1343-1370.
17. Kullback, S. (1959) Information Theory and Statistics. Mineola: Dover Publications.
18. Kullback, S. and Leibler, R. A. (1951) On information and sufficiency. Ann. Math. Statist., 22, 79-86.
19. Lee, P. M. (1997) Bayesian Statistics: an Introduction, 2nd edn. London: Arnold.
20. McCulloch, R. E. (1988) Information and the likelihood function in exponential families. Am. Statistn, 42, 73-75.
21. O'Hagan, A. (1998) Eliciting expert beliefs in substantial practical applications. Statistician, 47, 21-35.
22. O'Hagan, A., Glennie, E. B. and Beardsall, R. E. (1992) Subjective modelling and Bayes linear estimation in the UK water industry. Appl. Statist., 41, 563-577.
23. Phillips, L. D. and Edwards, W. (1966) Conservatism in a simple probability inference task. J. Exptl Psychol., 72, 346-354.
24. Raiffa, H. A. and Schlaifer, R. S. (1961) Applied Statistical Decision Theory. Boston: Harvard University.
25. Savage, L. J. (1971) Elicitation of personal probabilities and expectations. J. Am. Statist. Ass., 66, 783-801.
26. Simon, H. A. (1957) Models of Man: Social and Rational: Mathematical Essays on Rational Human Behavior in a Social Setting. New York: Wiley.
27. Smith, L. H. (1967) Ranking procedures and subjective probability distributions. Mangmnt Sci. B, 14, 236-249.
28. Soofi, E. S. (1994) Capturing the intangible concept of information. J. Am. Statist. Ass., 89, 1243-1254.
29. Staël von Holstein, C.-A. S. (1971) The effect of learning on the assessment of subjective probability distributions. Organznl Behav. Hum. Perform., 6, 304-315.
30. Wallsten, T. S. and Budescu, D. V. (1983) Encoding subjective probabilities: a psychological and psychometric review. Mangmnt Sci., 29, 151-173.
31. Winkler, R. L. (1967) The assessment of prior distributions in Bayesian analysis. J. Am. Statist. Ass., 67, 776-800.
32. Winkler, R. L., Smith, J. E. and Fryback, D. G. (2002) The role of informative priors in zero-numerator problems: being conservative versus being candid. Am. Statistn, 56, 1-4.
33. Winkler, R. L., Smith, W. S. and Kulkarni, R. B. (1978) Adaptive forecasting models based on predictive distributions. Mangmnt Sci., 24, 977-986.