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On the posterior distribution of a dirichlet process given randomly right censored observations

Author

Listed:
  • Blum, J.
  • Susarla, V.

Abstract

The purpose of this note is to show that the conditional distribution of a Dirichlet process P given n independent observations X1... Xn from P and belonging to measurable sets A1,... An with A1 [subset, double equals] A1+1 for i=1,... n=1 is a mixture of Dirichlet processes as introduced by Antoniak. It is also shown that this result is applicable in Bayesin decision problems concerning a random survival distribution under Dirichlet process priors.

Suggested Citation

  • Blum, J. & Susarla, V., 1977. "On the posterior distribution of a dirichlet process given randomly right censored observations," Stochastic Processes and their Applications, Elsevier, vol. 5(3), pages 207-211, July.
    • Handle: RePEc:eee:spapps:v:5:y:1977:i:3:p:207-211
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    Citations

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    Cited by:

    1. Ghosh, J. K. & Ramamoorthi, R. V. & Srikanth, K. R., 1999. "Bayesian analysis of censored data," Statistics & Probability Letters, Elsevier, vol. 41(3), pages 255-265, February.
    2. Antonio Lijoi & Igor Prunster, 2009. "Models beyond the Dirichlet process," Quaderni di Dipartimento 103, University of Pavia, Department of Economics and Quantitative Methods.
    3. Dean A. Follmann & Paul S. Albert, 1999. "Bayesian Monitoring of Event Rates with Censored Data," Biometrics, The International Biometric Society, vol. 55(2), pages 603-607, June.
    4. Antonio Lijoi & Igor Pruenster, 2009. "Models beyond the Dirichlet process," ICER Working Papers - Applied Mathematics Series 23-2009, ICER - International Centre for Economic Research.
    5. Chiara Gigliarano & Pietro Muliere, 2013. "Estimating the Lorenz curve and Gini index with right censored data: a Polya tree approach," METRON, Springer;Sapienza Università di Roma, vol. 71(2), pages 105-122, September.
    6. Victor Salinas & José Romeo & Alexis Peña, 2010. "On Bayesian estimation of a survival curve: comparative study and examples," Computational Statistics, Springer, vol. 25(3), pages 375-389, September.
    7. Richard L Warr & David H Collins, 2014. "Bayesian nonparametric models for combining heterogeneous reliability data," Journal of Risk and Reliability, , vol. 228(2), pages 166-175, April.
    8. Gary L. Rosner, 2005. "Bayesian Monitoring of Clinical Trials with Failure-Time Endpoints," Biometrics, The International Biometric Society, vol. 61(1), pages 239-245, March.
    9. Chenyang Zhang & Guosheng Yin, 2023. "Bayesian nonparametric analysis of restricted mean survival time," Biometrics, The International Biometric Society, vol. 79(2), pages 1383-1396, June.
    10. Neath, Andrew A. & Samaniego, Francisco J., 1997. "On Bayesian estimation of the multiple decrement function in the competing risks problem, II: The discrete case," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 345-354, November.

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