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Bayes Estimators in Group Testing

  • 발행 : 2004.12.01

초록

Binomial group testing or composite sampling is often used to estimate the proportion, p, of positive(infects, defectives) in a population when that proportion is known to be small; the potential benefits of group testing over one-at-a-time testing are well documented. The literature has focused on maximum likelihood estimation. We provide two Bayes estimators and compare them with the MLE. The first of our Bayes estimators uses an uninformative Uniform (0, 1) prior on p; the properties of this estimator are poor. Our second Bayes estimator uses a much more informative prior that recognizes and takes into account key aspects of the group testing context. This estimator compares very favorably with the MSE, having substantially lower mean squared errors in all of the wide range of cases we considered. The priors uses a Beta distribution, Beta ($\alpha$, $\beta$), and some advice is provided for choosing the parameter a and $\beta$ for that distribution.

키워드

참고문헌

  1. Bickel, P.L. and Doksum, K.A(1997). Mathematical Statistics. Holden-Day Inc.,419
  2. Casella, G. and Berger, RL.(1990). Statistical Inference. Wadworth and Brooks/Cole, 475
  3. Calhoon-Young, B., Chandler, A, LivelTI1ore, T., Gaudino, J, and Benjamin, R (1989). Sensitivity and specificity of pooled versus individual sera in a HN-antibody prevalence study. Jounal of Clinical Microbiology, 27, 1893-1895
  4. Chaloner, K. M. and Duncan, G. T. (1983). Assessment of a Beta prior distribution: PM elicitation. The Statistician, 32 174-180 https://doi.org/10.2307/2987609
  5. Chen, C. L. and Swallow, W. H. (1990). Using group testing to estimate a proportion and to test the binomial model. Biometrics 46, 1035-1046 https://doi.org/10.2307/2532446
  6. Chen, C. L. and Swallow, W. H. (1995). Sensitivity analysis of variable-size group testing and its related models. Biometrical Journal 37, 173-181 https://doi.org/10.1002/bimj.4710370207
  7. Emmanuel, J C., Bassett, M. T., Smith, H. J., and Jacob, J A (1988). Pooling of sera for HN testing: An economical method for use in developing countries. Journal of Clinical Pathology 41, 582-5 https://doi.org/10.1136/jcp.41.5.582
  8. Gibbs, A J and Gower, J C. (1960). The use of a multiple-tansfer method in plant virus transmission studies-Some statistical points arising in the analysis of results Annals of Applied Biology 48, 75-83
  9. Hung, M. and Swallow, W. H. (1999). Robustness of group testing in the estimation of proportions. Biometrics 55, 231-237 https://doi.org/10.1111/j.0006-341X.1999.00231.x
  10. Hwang, F. K. (1984). Robust group testing. Journal of Qualitative Technology 89, 189-195
  11. Kumar, S. and Sobel M. (1975). An asymtotocally optimal Bayes solution for group testing. In A Survey of Statistical Design and Latin Models, J N. Srivastava (ed,) , 367-381. Amsterdam: North Holland
  12. Le, C. T. (1981). A new estimator for infection rates using pools of variable size. American journal of Epidemiology 114, 132-136 https://doi.org/10.1093/oxfordjournals.aje.a113159
  13. Litvak, E., Tu, X. M., and Pagano, M. (1994). Screening for the presence of a disease by pooling sera samples. Journal of the American Statistical Association 89, 424-34 https://doi.org/10.2307/2290842
  14. Sobel, M. and Elasfoff, R. M. (1975). Group testing with a new goal, estimation. Biometrika 62, 1179-1252
  15. Sobel, M. and Groll, P. A. (1959). Group testing to eliminate efficiently all defectives in a binomial sample. The Bell System Technical Journal 38, 1179-1252 https://doi.org/10.1002/j.1538-7305.1959.tb03914.x
  16. Swallow, W. H. (1985). Group testing for estimating infection rates and probabilities of disease transmission. Phytopathology 75, 882-889 https://doi.org/10.1094/Phyto-75-882
  17. Thompson, K. H. (1962). Estimation of the population of vectors in a natural population of insects. Biometrics 18, 568-578 https://doi.org/10.2307/2527902
  18. Tu, X. M., Litvak, E., and Pagano, M. (1994). Screening tests: Can we get more by doing less. Statistics in Medicine 13, 1905-1919 https://doi.org/10.1002/sim.4780131904
  19. ______(1995). On the informativeness and accuracy of pooled testing in estimating prevalence of a rare disease: Application to HIV screening. Biometrika 82, 287-297 https://doi.org/10.1093/biomet/82.2.287
  20. Walter, S. D., Hildreth, S. W., and Beaty, B. J (1980). Estimation of infection rates in populations of organisms using pools of various size. Journal of Epidemiology 112, 124-128 https://doi.org/10.1093/oxfordjournals.aje.a112961