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Abstract

Collections of related Poisson or binomial counts arise, for example, from a number of different failures in similar machines or neighbouring time periods. A conventional Bayesian analysis requires a rather indirect prior specification and intensive numerical methods for posterior evaluations. An alternative approach using Bayes linear kinematics in which simple conjugate specifications for individual counts are linked through a Bayes linear belief structure is presented. Intensive numerical methods are not required. The use of transformations of the binomial and Poisson parameters is proposed. The approach is illustrated in two examples, one involving a Poisson count of failures, the other involving a binomial count in an analysis of failure times.

Keywords

Bayesian inference Bayes linear kinematics count data failure rates failure times

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References

Wang

P. C.

Comparisons on the analysis of Poisson data

Qual. Reliab. Engng Int. 1999 15 379–383

Fa-Si-Oen

Pievatolo

The analysis of ruptures in metropolitan gas pipelines

Qual. Reliab. Engng Int. 2000 16 17–22

Martz

H. F.

Kvam

P. H.

Abramson

L. R.

Empirical Bayes estimation of the reliability of nuclear-power-plant emergency diesel generators

Technometrics 1996 38 11–24

Dellaportas

Smith

A. F. M.

Bayesian inference for generalised linear and proportional hazards models via gibbs sampling

Appl. Stat. 1993 42 443–459

Clayton

D. G.

Gilks

W. R.

Richardson

Spiegelhalter

D. J.

Generalised linear mixed models

Markov Chain Monte Carlo in Practice 1996

New York

Chapman & Hall

275–301

Goldstein

Shaw

Bayes linear kinematics and Bayes linear Bayes graphical models

Biometrika 2004 91 425–446

10.

Müuller

Bernardo

J. M.

Berger

J. O.

Dawid

A. P.

Smith

A. F. M.

Simulation-based optimal design

In Bayesian statistics 6 1999

Oxford University Press

459–474

11.

West

Harrison

P. J.

Migon

H. S.

Dynamic generalized linear models and Bayesian forecasting

J. Am. Stat. Assoc. 1985 80 73–83

12.

13.

14.

15.

16.

Kadane

J. B.

Wolfson

L. J.

Experiences in elicitation

Statistician 1998 47 3–19

17.

Garthwaite

P. H.

O'Hagan

Quantifying expert opinion in the UK water industry: An experimental study

Statistician 2000 49 455–477

18.

Farrow

Practical building of subjective covariance structures for large complicated systems

Statistician 2003 52 553–573

19.

Garthwaite

P. H.

Kadane

J. B.

O'Hagan

Statistical methods for eliciting probability distributions

J. Am. Stat. Assoc. 2005 100 680–700

20.

Peterson

C. R.

Snapper

K. J.

Murphy

A. H.

Credible interval temperature forecasts

Bull. Am. Meteorol. Soc. 1972 53 966–970

21.

Murphy

A. H.

Winkler

R. L.

Reliability of subjective probability forecasts of precipitation and temperature

Appl. Stat. 1977 26 41–47

22.

Barclay

Peterson

C. R.

Two methods for assessing probability distributions. Technical Report 73-1, Decisions and Designs Inc., McLean Virginia, USA, 1973

23.

Spiropoulos

Decision support for management using Bayes linear influence diagrams PhD Thesis, University of Sunderland, 1995

24.

Goldstein

Farrow

Spiropoulos

Prediction under the in uence: Bayes linear in uence diagrams for prediction in a large brewery

Statistician 1993 42 445–459

25.

26.

27.

28.

Gamerman

Dynamic Bayesian models for survival data

Appl. Stat. 1991 40 63–79

Bayes linear kinematics in the analysis of failure rates and failure time distributions

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