Bayesian updating for binary variables: An application in the UK water industry

Journal of the Royal Statistical Society Series D: The Statistician

Volumn 52, Issue 4, 2003, Pages 483-499

  Papathomas, Michail ^a,c   Hocking, Roger J ^b  

^a UNIVERSITY OF SHEFFIELD   (United Kingdom)

^b South West Water ^*  (United Kingdom)

^c UNIVERSITY OF THE AEGEAN   (Greece)

Author keywords

Asset management; Binary variables; Elicitation; Expert opinion; Probability assessments

Indexed keywords

EID: 0347588128     PISSN: 00390526     EISSN: None     Source Type: Journal    
DOI: 10.1046/j.0039-0526.2003.00451.x     Document Type: Article

References (33)

1. Agresti, A. (1990) Categorical Data Analysis. New York: Wiley.
2. Cloteaux, B., Eick, C. and Kreinovich, V. (1998) From ordered beliefs to numbers: how to elicit numbers without asking for them (doable but computationally difficult). Int. J. Intell. Syst., 13, 801-820.
3. Cooke, R. M. (1991) Experts in Uncertainty: Opinion and Subjective Probability in Science. Oxford: Oxford University Press.
4. Craig, P. S., Goldstein, M., Seheult, A. H. and Smith, J. A. (1996) Bayes linear strategies for matching hydrocarbon reservoir history. In Bayesian Statistics 5 (eds J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith), pp. 69-95. Oxford: Oxford University Press.
5. Dall'Aglio, G., Kotz, S. and Salinetti, G. (eds) (1991) Advances in Probability Distributions with Given Marginals. Dordrecht: Kluwer.
6. de Finetti, B. (1974) Theory of Probability, vol. 1. London: Wiley.
7. Garthwaite, P. H. (1994) Assessment of prior distributions for regression models: an experimental study. Communs Statist. Simuln, 23, 871-895.
8. Garthwaite, P. H. and Dickey, J. M. (1996) Elicitations of prior distributions for variable-selection problems in regression. Ann. Statist., 20, 1697-1719.
9. Garthwaite, P. H. and O'Hagan, A. (2000) Quantifying expert opinion in the UK water industry: an experimental study. Statistician, 49, 455-477.
10. Gilks, W. R. and Wild, P. (1992) Adaptive rejection sampling for Gibbs sampling. Appl. Statist., 41, 337-348.
11. Goldstein, M. (1999) Bayes linear analysis. In Encyclopedia of Statistical Sciences, update vol. 3 (eds S. Kotz, C. B. Read and D. L. Banks), pp. 29-34. Chichester: Wiley.
12. Goldstein, M. and O'Hagan, A. (1996) Bayes linear sufficiency and systems of expert posterior assessments. J. R. Statist. Soc. B, 58, 301-316.
13. Goldstein, M. and Wilkinson, D. J. (2000) Bayes linear analysis for graphical models: the geometric approach to local computation and interpretive graphics. Statist. Comput., 10, 311-324.
14. Hogarth, R. M. (1975) Cognitive processes and the assessment of subjective probability distributions. J. Am. Statist. Ass., 70, 271-294.
15. Howson, C. and Urbach, P. (1989) Scientific Reasoning: the Bayesian Approach. La Salle: Open Court.
16. Jeffrey, R. C. (1983) The Logic of Decision, 2nd edn. Chicago: University of Chicago Press.
17. 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.
18. Landrum, M. B. and Normand, S. T. (1999) Applying Bayesian ideas to the development of medical guidelines. Statist. Med., 18, 117-137.
19. Madigan, D., Gavrin, J. and Raftery, A. E. (1995) Eliciting prior information to enhance the predictive performance of Bayesian graphical models. Communs Statist. Theory Meth., 24, 2271-2292.
20. Meyer, M. and Booker, J. (1981) Knowledge-based Expert Systems, vol. 5, Eliciting and Analyzing Expert Judgement: a Practical Guide. New York: Academic Press.
21. Nelsen, R. B. (1999) An Introduction to Copulas. New York: Springer.
22. Ochi, Y. and Prentice, R. L. (1984) Likelihood inference in a correlated probit regression model. Biometrika, 71, 531-543.
23. O'Hagan, A. (1988) Probability: Methods and Measurement. London: Chapman and Hall.
24. O'Hagan, A. (1994) Robust modelling for asset management. J. Statist. Planng Inf., 40, 245-259.
25. O'Hagan, A. (1995) The ABLE story: Bayesian asset management in the water industry. Technical Report 1995-10. Department of Mathematics, University of Nottingham, Nottingham.
26. O'Hagan, A. (1998) Eliciting expert beliefs in substantial practical applications. Statistician, 47, 21-35.
27. 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.
28. Papathomas, M. (2001) Non-parametric Bayesian procedures for binary random variables. PhD Thesis. University of Sheffield, Sheffield.
29. Papathomas, M. and O'Hagan, A. (2001) Updating beliefs for binary random variables using a non-parametric Bayesian procedure. Research Report 509/01. University of Sheffield, Sheffield.
30. Regan, M. M. and Catalano, P. J. (1999) Likelihood models for clustered binary and continuous outcomes: application to developmental toxicology. Biometrics, 55, 760-768.
31. Renooij, S. and Witteman, C. (1999) Talking probabilities: communicating probabilistic information with words and numbers. Int. J. Approx. Reasng, 22, 169-194.
32. Shaw, S. C. and Goldstein, M. (2002) Augmented Bayes linear/Bayes graphical models. Durham University, Durham. (Available from http://maths.dur.ac.uk/stats/people/scs/blb.pdf.)
33. Williams, P. M. (1980) Bayesian conditionalisation and the principle of minimum information. Br. J. Philos. Sci., 31, 131-144.