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Latent diffusion models for event history analysis
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Roberts, Gareth O. and Sangalli, Laura M. (2007) Latent diffusion models for event history analysis. Working Paper. University of Warwick. Centre for Research in Statistical Methodology, Coventry.
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Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
Abstract
We consider Bayesian hierarchical models for event history analysis, where the event times are modeled through an underlying diffusion process, which determines the hazard rate. We show how these models can be e±ciently treated by means of Markov chain Monte Carlo techniques.
| Item Type: | Working or Discussion Paper (Working Paper) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Statistics |
| Library of Congress Subject Headings (LCSH): | Diffusion processes, Survival analysis (Biometry) |
| Series Name: | Working papers |
| Publisher: | University of Warwick. Centre for Research in Statistical Methodology |
| Place of Publication: | Coventry |
| Date: | 2007 |
| Volume: | Vol.2007 |
| Number: | No.27 |
| Number of Pages: | 17 |
| Status: | Not Peer Reviewed |
| Access rights to Published version: | Open Access |
| Funder: | European Commission (EC), University of Warwick. Centre for Research in Statistical Methodology |
| References: | Aalen, O. O. and Gjessing, H. K. (2001), \Understanding the shape of the hazard rate: a process point of view," Statist. Sci., 16, 1{22, with comments and a rejoinder by the authors. | (2004), \Survival models based on the Ornstein-Uhlenbeck process," Lifetime Data Anal., 10, 407{423. Beskos, A., Papaspiliopoulos, O., Roberts, G. O., and Fearnhead, P. (2006), \Exact and computationally e±cient likelihood-based estimation for discretely observed di®usion processes," J. R. Statist. Soc. B, to appear. Cox, D. R. (1972), \Regression models and life-tables," J. Roy. Statist. Soc. Ser. B, 34, 187{220, with discussion by F. Downton, Richard Peto, D. J. Bartholomew, D. V. Lindley, P. W. Glassborow, D. E. Barton, Susannah Howard, B. Benjamin, John J. Gart, L. D. Meshalkin, A. R. Kagan, M. Zelen, R. E. Barlow, Jack Kalb°eisch, R. L. Prentice and Norman Breslow, and a reply by D. R. Cox. Damien, P. and Walker, S. (2002), \A Bayesian non-parametric comparison of two treatments," Scand. J. Statist., 29, 51{56. Doksum, K. (1974), \Tailfree and neutral random probabilities and their posterior distributions," Ann. Probability, 2, 183{201. Elerian, O., Chib, S., and Shephard, N. (2001), \Likelihood inference for discretely observed nonlinear di®usions," Econometrica, 69, 959{993. Freireich, E. O. (1963), \The e®ect of 6 mercaptopurine on the duration of steroid induced remission in acute leukemia," Blood, 21, 699{716. Gehan, E. A. (1965), \A generalized Wilcoxon test for comparing arbitrarily singly-censored samples," Biometrika, 52, 203{223. Gelfand, A. E., Sahu, S. K., and Carlin, B. P. (1995), \E±cient parameterisations for normal linear mixed models," Biometrika, 82, 479{488. | (1996), \E±cient parametrizations for generalized linear mixed models," in Bayesian statistics, 5 (Ali- cante, 1994), New York: Oxford Univ. Press, Oxford Sci. Publ., pp. 165{180. Hills, S. E. and Smith, A. F. M. (1992), \Parameterization issues in Bayesian inference," in Bayesian statistics, 4 (Pe~n¶³scola, 1991), New York: Oxford Univ. Press, pp. 227{246. Hjort, N. L. (1990), \Nonparametric Bayes estimators based on beta processes in models for life history data," Ann. Statist., 18, 1259{1294. Kalb°eisch, J. D. (1978), \Non-parametric Bayesian analysis of survival time data," J. Roy. Statist. Soc. Ser. B, 40, 214{221. Kloeden, P. E. and Platen, E. (1992), Numerical solution of stochastic di®erential equations, vol. 23 of Applications of Mathematics (New York), Berlin: Springer-Verlag. Laud, P. W., Damien, P., and Smith, A. F. M. (1998), \Bayesian nonparametric and covariate analysis of failure time data," in Practical nonparametric and semiparametric Bayesian statistics, New York: Springer, vol. 133 of Lecture Notes in Statist., pp. 213{225. Myers, L. E. (1981), \Survival functions induced by stochastic covariate processes," J. Appl. Probab., 18, 523{529. Papaspiliopoulos, O., Roberts, G. O., and SkÄold, M. (2003), \Non-centered parameterizations for hierarchi- cal models and data augmentation," in Bayesian statistics, 7 (Tenerife, 2002), New York: Oxford Univ. Press, pp. 307{326, with a discussion by Alan E. Gelfand, Ole F. Christensen and Darren J. Wilkinson, and a reply by the authors. | (2007), \A general framework for the parametrization of Hierarchical models," Statit. Sci., 22, 59{73. Roberts, G. O. and Stramer, O. (2001), \On inference for partially observed nonlinear di®usion models using the Metropolis-Hastings algorithm," Biometrika, 88, 603{621. Rogers, L. C. G. and Williams, D. (2000), Di®usions, Markov processes, and martingales. Vol. 2, Cam- bridge Mathematical Library, Cambridge: Cambridge University Press, it^o calculus, Reprint of the second (1994) edition. Shephard, N. and Pitt, M. K. (1997), \Likelihood analysis of non-Gaussian measurement time series," Biometrika, 84, 653{667. Wei, L. J. (1984), \Testing goodness of ¯t for proportional hazards model with censored observations," J. Amer. Statist. Assoc., 79, 649{652. Woodbury, M. A. and Manton, K. G. (1977), \A random-walk model of human mortality and aging," Theoret. Population Biology, 11, 37{48. Xu, R. and O'Quigley, J. (2000), \Proportional hazards estimate of the conditional survival function," J. R. Stat. Soc. Ser. B Stat. Methodol., 62, 667{680. Yashin, A. I. (1985), \Dynamics of survival analysis: conditional Gaussian property versus the Cameron- Martin formula," in Statistics and control of stochastic processes (Moscow, 1984), New York: Optimiza- tion Software, Transl. Ser. Math. Engrg., pp. 466{485. Yashin, A. I. and Vaupel, J. W. (1986), \Measurement and estimation in heterogeneous populations," in Immunology and epidemiology (Mogilany, 1985), Berlin: Springer, vol. 65 of Lecture Notes in Biomath., pp. 198{206. |
| URI: | http://wrap.warwick.ac.uk/id/eprint/35559 |
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