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Markov Beta and Gamma Processes for Modelling Hazard Rates

Author

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  • LUIS E. NIETO‐BARAJAS
  • STEPHEN G. WALKER

Abstract

This paper generalizes the discrete time independent increment beta process of Hjort (1990), for modelling discrete failure times, and also generalizes the independent gamma process for modelling piecewise constant hazard rates (Walker and Mallick, 1997). The generalizations are from independent increment to Markov increment prior processes allowing the modelling of smoothness. We derive posterior distributions and undertake a full Bayesian analysis.

Suggested Citation

  • Luis E. Nieto‐Barajas & Stephen G. Walker, 2002. "Markov Beta and Gamma Processes for Modelling Hazard Rates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 413-424, September.
    • Handle: RePEc:bla:scjsta:v:29:y:2002:i:3:p:413-424
    DOI: 10.1111/1467-9469.00298
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    Citations

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    Cited by:

    1. Luis E. Nieto-Barajas, 2022. "Bayesian nonparametric dynamic hazard rates in evolutionary life tables," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(2), pages 319-334, April.
    2. Gianni Amisano & Roberto Casarin, 2008. "Particle Filters for Markov-Switching Stochastic-Correlation Models," Working Papers 0814, University of Brescia, Department of Economics.
    3. Antonio Lijoi & Igor Prunster, 2009. "Models beyond the Dirichlet process," Quaderni di Dipartimento 103, University of Pavia, Department of Economics and Quantitative Methods.
    4. Nieto-Barajas, Luis E. & Walker, Stephen G., 2007. "A Bayesian semi-parametric bivariate failure time model," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6102-6113, August.
    5. Bhattacharjee, Arnab & Bhattacharjee, Madhuchhanda, 2007. "Bayesian Analysis of Hazard Regression Models under Order Restrictions on Covariate Effects and Ageing," MPRA Paper 3938, University Library of Munich, Germany.
    6. Martínez-Ovando Juan Carlos & Walker Stephen G., 2011. "Time-series Modelling, Stationarity and Bayesian Nonparametric Methods," Working Papers 2011-08, Banco de México.
    7. Luis Nieto-Barajas & Eduardo Gutiérrez-Peña, 2022. "General dependence structures for some models based on exponential families with quadratic variance functions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 699-716, September.
    8. Luis E. Nieto-Barajas & Peter Müller & Yuan Ji & Yiling Lu & Gordon B. Mills, 2012. "A Time-Series DDP for Functional Proteomics Profiles," Biometrics, The International Biometric Society, vol. 68(3), pages 859-868, September.
    9. Nieto-Barajas, Luis E. & Walker, Stephen G., 2007. "Gibbs and autoregressive Markov processes," Statistics & Probability Letters, Elsevier, vol. 77(14), pages 1479-1485, August.
    10. Peter Müeller & Fernando A. Quintana & Garritt Page, 2018. "Nonparametric Bayesian inference in applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 175-206, June.
    11. Bhattacharjee, Arnab & Bhattacharjee, Madhuchhanda, 2007. "Bayesian Analysis of Hazard Regression Models under Order Restrictions on Covariate Effects and Ageing," MPRA Paper 3938, University Library of Munich, Germany.
    12. Hachem, Hassan & Vu, Hai Canh & Fouladirad, Mitra, 2024. "Different methods for RUL prediction considering sensor degradation," Reliability Engineering and System Safety, Elsevier, vol. 243(C).
    13. Thomas A. Murray & Peter F. Thall & Ying Yuan & Sarah McAvoy & Daniel R. Gomez, 2017. "Robust Treatment Comparison Based on Utilities of Semi-Competing Risks in Non-Small-Cell Lung Cancer," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 11-23, January.
    14. Michael L. Pennell & David B. Dunson, 2006. "Bayesian Semiparametric Dynamic Frailty Models for Multiple Event Time Data," Biometrics, The International Biometric Society, vol. 62(4), pages 1044-1052, December.
    15. de Alba, Enrique & Nieto-Barajas, Luis E., 2008. "Claims reserving: A correlated Bayesian model," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 368-376, December.
    16. Luis E. Nieto‐Barajas & Guosheng Yin, 2008. "Bayesian Semiparametric Cure Rate Model with an Unknown Threshold," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 540-556, September.
    17. Kaeding, Matthias, 2020. "Efficient Bayesian nonparametric hazard regression," Ruhr Economic Papers 850, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    18. Luca La Rocca, 2008. "Bayesian Non‐Parametric Estimation of Smooth Hazard Rates for Seismic Hazard Assessment," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(3), pages 524-539, September.

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