Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Bayesian Inference for Multinomial Group Testing

  • Heo, Tae-Young (Electronics and Telecommunications Research Institute) ;
  • Kim, Jong-Min (Division of Science and Mathematics, University of Minnesota-Morris)
  • Published : 2007.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper consider trinomial group testing concerned with classification of N given units into one of k disjoint categories. In this paper, we propose Bayesian inference for estimating individual category proportions using the trinomial group testing model proposed by Bar-Lev et al. (2005). We compared a relative efficience (RE) based on the mean squared error (MSE) of MLE and Bayes estimators with various prior information. The impact of different prior specifications on the estimates is also investigated using selected prior distribution. The impact of different priors on the Bayes estimates is modest when the sample size and group size we large.

Keywords

References

  1. Bar-Lev, S. K., Stadje, W. and van der Duyn Schouten, F. A. (2005). Multinomial group testing models with incomplete identification. Journal of Statistical Planning and Inference, 135, 384-401 https://doi.org/10.1016/j.jspi.2004.05.011
  2. Chaubey, Y. P. and Li, W. (1995). Comparison between maximum likelihood and Bayes methods for estimation of binomial probability with sample compositing. Journal of Official Statistics, 11, 379-390
  3. Chick, S. E. (1996). Bayesian models for limiting dilution assay and group test data. Biometrics, 52, 1055-1062 https://doi.org/10.2307/2533066
  4. Dorfman, R. (1943). The detection of defective members of large populations. The Annals of Mathematical Statistics, 14,436-440 https://doi.org/10.1214/aoms/1177731363
  5. Hughes-Oliver, J. M. and Rosenberger, W. F. (2000). Efficient estimation of the prevalence of multiple rare traits. Biometrika, 87, 315-327 https://doi.org/10.1093/biomet/87.2.315
  6. Kumar, S. (1970a). Multinomial group-testing. SIAM Journal of on Applied Mathematics, 19, 340-350 https://doi.org/10.1137/0119032
  7. Kumar, S. (1970b). Group-testing to classify all units in a trinomial sample. Studia Scientiarum Mathematicarum Hungarica, 5, 229-247
  8. Kumar, S. (1972). Trinomial group-testing with an unknown proportion of units in the three categories. Annals of the Institute of Statistical Mathematics, 24, 171-181 https://doi.org/10.1007/BF02479748
  9. Kwon, S. (2004). Bayes estimators in group testing. The Korean Communication in Statistics, 11, 619-630 https://doi.org/10.5351/CKSS.2004.11.3.619
  10. Pfeiffer, R. M., Rutter, J. L., Gail, M., Struewing, J. and Gastwirth, J. L. (2002). Efficiency of DNA pooling to estimate joint allele frequencies and measure linkage disequilibrium. Genetic Epidemiology, 22, 94-102 https://doi.org/10.1002/gepi.1046
  11. Tebbs, J. M., Bilder, C. R. and Moser, B. K. (2003). An empirical Bayes group-testing approach to estimating small proportions. Communications in Statistics: Theory and Methods, 32, 983-995 https://doi.org/10.1081/STA-120019957
  12. Xie, M. (2001). Regression analysis of group testing samples. Statistics in Medicine, 20, 1957-1969 https://doi.org/10.1002/sim.817
  13. Zhu, L., Hughes-Oliver, J. M. and Young, S. S. (2001). Statistical decoding of potent pools based on chemical structure. Biometrics, 57, 922-930 https://doi.org/10.1111/j.0006-341X.2001.00922.x