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Discovery Sampling and Selection Models

  • Mike West

Abstract

Various aspects of Bayesian inference in selection and size biased sampling problems are presented, beginning with discussion of general problems of inference in infinite and finite populations subject to selection sampling. Estimation of the size of finite populations and inference about superpopulation distributions when sampling is apparently informative is then developed in two specific problems. The first is a simple example of truncated data analysis, and some details of simulation based Bayesian analysis are presented. The second concerns discovery sampling in which units of a finite population are selected with probabilities proportional to some measure of size. A well known area of application is in the discovery of oil reserves, and some recently published data from this area is analysed here. Solutions to the computational problems arising are developed using iterative simulation methods. Finally, some comments are made on extensions, including multiparameter superpopulations, semi-parametric models and problems of dealing with missing data in discovery sampling.

Keywords

Joint Density Finite Mixture Finite Population Data Augmentation Predictive Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Bayarri, M. J. and DeGroot, M. H. (1987). Bayesian analysis of selection models. The Statistician 36, 137–146.CrossRefGoogle Scholar
  2. Escobar, M. D., and West, M. (1992). Bayesian density estimation and inference using mixtures. Invited revision for J. Amer. Statist. Assoc.Google Scholar
  3. Gelfand, A. E., and Smith, A. F. M. (1990). Sampling based approaches to calculating marginal densities. J. Amer. Statist. Assoc. 85, 398–409.MathSciNetMATHCrossRefGoogle Scholar
  4. Irony, T. Z. (1992). Information in sampling rules. J. Stat. Plan. Inf. (to appear).Google Scholar
  5. Kuo, L., and Smith, A. F. M. (1992). Bayesian computations in survival models via the Gibbs sampler. In Survival Analysis: State of the Art, J. P. Klein and P. K. Goel (eds.). Kluwer.Google Scholar
  6. Nair, V. J., and Wang, P. C. C. (1989). Maximum likelihood estimation under a successive sampling discovery model. Technometrics 31, 423–436.MathSciNetMATHCrossRefGoogle Scholar
  7. Raftery, A., and Lewis, S. (1992). How many iterations in the Gibbs sampler? In Bayesian Statistics IV, J. O. Berger, J. M. Bernardo, A. P. Dawid and A. F. M. Smith (eds.). Oxford University Press.Google Scholar
  8. Sanathanan, L. (1977). Estimating the size of a truncated sample. J. Amer. Statist. Assoc. 72, 669–672.MathSciNetMATHCrossRefGoogle Scholar
  9. Tanner, M. A., and Wong, W. H. (1987). The calculation of posterior distributions by data augmentation (with discussion). J. Amer. Statist. Assoc. 82, 528–550.MathSciNetMATHCrossRefGoogle Scholar
  10. West, M. (1992). Bayesian analysis of a discovery model. ISDS discussion paper, Duke University.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1994

Authors and Affiliations

  • Mike West
    • 1
  1. 1.Duke UniversityUSA

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