Non-Homogeneous Poisson Processes Applied to Count Data: A Bayesian Approach Considering Different Prior Distributions

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References

[1] J. A. Achcar, K. D. Dey and M. Niverthi, “A Bayesian Approach Using Nonhomogeneous Poisson Process for Software Reliability Models,” In: A. S. Basu, S. K. Basu and S. Mukhopadhyay, Eds., Frontiers in Reliability, World Scientic Publishing Co., Singapore, 1998, pp. 1- 18. doi:10.1142/9789812816580_0001

[2] A. L. Goel and K. Okumoto, “An Analysis of Recurrent Software Errors in a Real-Time Control System,” Proceedings of the 1978 Annual Conference, ACM’78, Washington DC, 4-6 December 1978, pp. 496-501.
doi:10.1145/800127.804160

[3] A. L. Goel, “A Guidebook for Software Reliability Assessment,” Technical Report, Syracuse University, Sy- racse, 1983.

[4] G. S. Muldholkar, D. K. Srivastava and M. Friemer, “The Exponentiated-Weibull Family: A Reanalysis of the Bus- Motor Failure Data,” Technometrics, Vol. 37, No. 4, 1995, pp. 436-445. doi:10.1080/00401706.1995.10484376

[5] V. G. Cancho, H. Bolfarine and J. A. Achcar, “A Bayesian Analysis of the Exponentiated-Weibull Distribution,” Journal of Applied Statistical Science, Vol. 4, 1999, pp. 227-242.

[6] J. E. R. Cid and J. A. Achcar, “Bayesian Inference for Non- homogeneous Poisson Processes in Software Reliability Models Assuming Nonmonotonic Intensity Functions,” Computational Statistics and Data Analysis, Vol. 32, No. 2, 1999, pp. 147-159.doi:10.1016/S0167-9473(99)00028-6

[7] A. Gelman and D. R. Rubin, “A Single Series from the Gibbs Sampler Provides a False Sense of Security,” In: J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, Eds., Bayesian Statistics 4, Oxford University Press, Oxford, 1992, pp. 625-631.

[8] S. P. Brook and A. Gelman, “General Methods for Monitoring Convergence of Iterative Simulations,” Journal of Computational and Graphical Statistics, Vol. 7, No. 4, 1997, pp. 434-455. doi:10.2307/1390675

[9] A. Gelman “Inference and Monitoring Convergence,” In: W. R. Gilks, S. Richardson and D. J. Spiegelhalter, Eds., Markov Chain Monte Carlo in Practice, Chapman and Hall, London, 1996, pp. 131-143.

[10] D. R. Cox and P. A. Lewis, “Statistical Analysis of Series of Events,” Methuen, London, 1966.
doi:10.1063/1.1699114

[11] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, “Equations of State Calculations by Fast Computing Machines,” Journal of Chemical Physics, Vol. 21, No. 6, 1953, pp. 1087-1092.doi:10.1063/1.1699114

[12] W. K. Hastings, “Monte Carlo Sampling Methods Using Markov Chains and Their Applications,” Biometrika, Vol. 57, No. 1, 1970, pp. 97-109. doi:10.1093/biomet/57.1.97

[13] G. Casella, and R. L. Berger, “Statistical Inference,” 2nd Edition, Duxbury Press, Pacific Grove, 2001.

[14] J. A. Achcar, E. R. Rodrigues, C. D. Paulino and P. Soares, “Non-homogeneous Poisson Models With a Change-Point: An Application to Ozone Peaks in Mexico City,” Environmental and Ecological Statistics, Vol. 17, No. 4, 2010, pp. 521-541.
doi:10.1007/s10651-009-0114-3