Bayesian computation of software reliability

Journal of Computational and Graphical Statistics

Volumn 4, Issue 1, 1995, Pages 65-82

  Kuo, Lynn ^a   Yang, Tae ^a  

^a UNIVERSITY OF CONNECTICUT   (United States)

Author keywords

Gibbs sampling; Hierarchical Bayes; Model selection; Stochastic substitution

Indexed keywords

EID: 0002977667     PISSN: 10618600     EISSN: 15372715     Source Type: Journal    
DOI: 10.1080/10618600.1995.10474666     Document Type: Article

References (32)

1. Abdel-Ghaly, A. A., Chan, P. Y., and Littlewood, B. (1986), “Evaluation of Competing Software Reliability Predictions,” IEEE Transactions on Software Engineering, 12, 950-967.
2. Blumenthal, S., and Marcus, R. (1975), “Estimating Population Size with Exponential Failure,” Journal of the American Statistical Association, 70, 913-922.
3. Box, G. (1980), “Sampling and Bayes’ Inference in Scientific Modeling and Robustness” (with discussion), Journal of the Royal Statistical Society, Ser. A, 143, 382—430.
4. Casella, G., and George, E. I. (1992), “Explaining the Gibbs Sampler,” The American Statistician, 46, 167-174.
5. Dawid, A. P. (1984), “Statistical Theory: The Prequential Approach,” Journal of the Royal Statistical Society, Ser. A, 147, 278-292.
6. Geisser, S., and Eddy, W. (1979), “A Predictive Approach to Model Selection,” Journal of the American Statistical Association, 74, 153-160.
7. Gelfand, A. E., Dey, D. K., and Chang, H. (1992), “Model Determination Using Predictive Distributions with Implementation via Sampling-Based Methods” (with discussion), in Bayesian Statistics 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Cambridge, MA: Oxford University Press, pp. 147-169.
8. Gelfand, A. E., and Smith, A. F. M. (1990), “Sampling-Based Approaches to Calculating Marginal Densities,” Journal of the American Statistical Association, 85, 398 -399.
9. Gelman, A. E., and Rubin D. (1992), “Inference from Iterative Simulation Using Multiple Sequences,” Statistical Science, 7, 457-472.
10. Geman, S., and Geman, D. (1984), “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
11. Goel, A. L., and Okumoto, K. (1979), “Time Dependent Error Detection Rate Model for Software Reliability and Other Performance Measures,” IEEE Transactions on Reliability, 28, 206-211.
12. Jelinski, Z., and Moranda, P. B. (1972), “Software Reliability Research,” in Statistical Computer Performance Evaluation, ed. W. Freiberger, New York: Academic Press, pp. 465—497.
13. Jewell, W. S. (1985), “Bayesian Extension to a Basic Model of Software Reliability,” IEEE Transactions on Software Engineering, 11, 1465-1471.
14. Joe, H., and Reid, N. (1985a), “Estimating the Number of Faults in a System,” Journal of the American Statistical Association, 80, 222—226.
15. Joe, H. (1985b), “On the Software Reliability Models of Jelinski-Moranda and Littlewood,” IEEE Transactions on Reliability, 34, 216-218.
16. Kalos, M. H., and Whitlock, P. A. (1986), Monte Carlo Methods, New York: John Wiley.
17. Kuo, L., and Cohen, M. P. (1992), “Bayesian Analysis for Linearized Multi-stage Models in Quantal Bioassay,” Technical Report No. 92-31, University of Connecticut, Statistics Dept.
18. Kuo, L., and Yang, T. (1993), “Bayesian Computation of Software Reliability,” Technical Report No. 93-18, University of Connecticut, Statistics Dept.
19. Langberg, N., and Singpurwalla, N. D. (1985), “A Unification of Some Software Reliability Models,” SIAM Journal on Scientific and Statistical Computing, 6, 781-790.
20. Littlewood, B. (1990), “Software Reliability Growth Models,” in Software Reliability Handbook, ed. P. Rook, London: Elsevier Applied Science, pp. 401—112.
21. Littlewood, B., and Sofer, A. (1987), “A Bayesian Modification to the Jelinski-Moranda Software Reliability Growth Model,” IEE/BCS Software Engineering Journal, 3, 30—41.
22. Littlewood, B., and Verrall, J. L. (1973), “A Bayesian Reliability Growth Model for Computer Software,” in Conference Record, 1973 IEEE Symposium on Computer Software Reliability, New York, pp. 70-76.
23. Mazzuchi, T.A., and Soyer, R. (1988), “A Bayes Empirical-Bayes Model for Software Reliability,” IEEE Transactions on Reliability, 37, 248—254.
24. Meinhold, R. J., and Singpurwalla, N. D. (1983), “Bayesian Analysis of a Commonly Used Model for Describing Software Failures,” The Statistician, 32, 168-173.
25. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953), “Equation of State Calculations by Fast Computing Machines,” Journal of Chemical Physics, 21, 1087-1092.
26. Pettit, L. I., and Young, K. D. S. (1990), “Measuring the Effects of Observations on Bayes Factors,” Biometrika, 77, 455—166.
27. Raftery, A. E. (1987), “Inference and Prediction for a General Order Statistic Model with Unknown Population Size,” Journal of the American Statistical Association, 82, 1163-1168.
28. Stone, M. (1974), “Cross-Validatory Choice and Assessment of Statistical Predictions,” Journal of the Royal Statistical Society, Ser. B, 111-147.
29. Tanner, M., and Wong, W. (1987), “The Calculation of Posterior Distributions by Data Augmentation” (with discussion), Journal of the American Statistical Association, 81, 82-86.
30. Thomas, A., Spiegelhalter, D. J., and Gilks, W. R. (1992), “BUGS: A Program to Perform Bayesian Inference using Gibbs Sampling,” in Bayesian Statistics 4, eds. J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, Cambridge, MA: Oxford University Press, pp. 837-842.
31. Tierney, L. (1991), “Markov Chains for Exploring Posterior Distributions,” Technical Report No. 560, University of Minnesota, School of Statistics.
32. Whittaker, J. (1990), Graphical Models in Applied Multivariate Statistics, New York: John Wiley.