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Beta Processes and Survival Analysis
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 Title & Authors
Beta Processes and Survival Analysis
Kim, Yongdai; Chae, Minwoo;
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This article is concerned with one of the most important prior distributions for Bayesian analysis of survival and event history data, called Beta processes, proposed in Hjort (1990). We review the current state of the art of beta processes and their application to survival analysis. Relevant methodological and practical areas of research that we touch on relate to constructions, posterior distributions, large-sample properties, Bayesian computations, and mixtures of Beta processes.
Beta processes;event history analysis;hazard rates;survival analysis;
 Cited by
Andersen, P. K., Borgan, O, Gill, R. D. and Keiding, N. (1993). Statistical Models Based on Counting Processes, Springer, New York.

Barron, A. R. (1988). The exponential convergence of posterior probabilities with implications for Bayes estimators of density functions, Technical report, University of Illinois.

Barron, A., Schervish, M. J. and Wasserman, L. (1999). The consistency of posterior distributions in nonparametric problems, Annals of Statistics, 27, 536-561. crossref(new window)

Damien, P., Laud, P. W. and Smith, A. F. M. (1996). Implementation of Bayesian non-parametric inference based on Beta processes, Scandinavian Journal of Statistics, 23, 27-36.

De Blasi, P., Favaro, S. and Muliere, P. (2009). A class of neutral to the right priors induced by superposition of beta processes, Working paper of Collegio Carlo Alberto.

De Blasi, P., Hjort, N. L. (2007). Bayesian survival analysis in proportional hazard models with logistic relative risks, Scandinavian Journal of Statistics, 34, 229-257. crossref(new window)

Diaconis, P. and Freedman, D. A. (1986). On the consistency of Bayes estimates, Annals of Statistics, 14, 1-26. crossref(new window)

Doksum, K. A. (1974). Tailfree and neutral random probabilities and their posterior distributions, Annals of Probability, 2, 183-201. crossref(new window)

Doss, H. (1994). Bayesian nonparametric estimation for incomplete data via successive substitution sampling, Annals of Statistics, 22, 1763-1786. crossref(new window)

Ferguson, T. S. (1973). A Bayesian analysis of some nonparametric problems, Annals of Statistics, 1, 209-230. crossref(new window)

Ferguson. T. S. and Phadia, E. G. (1979). Bayesian nonparametric estimation based on censored data, Annals of Statistics, 7, 163-186. crossref(new window)

Ghosal, S., Ghosh, J. K. and Ramamoorthi, R. V. (1999). Posterior consistency of Dirichlet mixtures in density estimation, Annals of Statistics, 27, 143-158. crossref(new window)

Ghosal, S., Ghosh, J. K. and van der Vaart, A. D. (2000). Convergence rates of posterior distributions, Annals of Statistics, 28, 500-531. crossref(new window)

Ghosh, J. K. and Ramamoorthi, R. V. (2003). Bayesian Nonparametircs, Springer.

Gilks, W. R. and Wild, P. (1992). Adaptive rejection sampling for Gibbs sampling, Applied Statistics, 41, 337-348. crossref(new window)

Gill, R. D. and Johansen, S. (1990). A survey of product-integration with a view toward application in survival analysis, Annals of Statistics, 18, 1501-1555. crossref(new window)

Hjort, N. L. (1985). Contribution to the discussion of Andersen and Borgan's 'Counting process models for life history data: a review', Scandinavian Journal of Statistics, 12, 141-150.

Hjort, N. L. (1986). Contribution to the discussion of Diaconis and Freedman's 'On the consistency of Bayes estimates', Annals of Statistics, 14, 49-55. crossref(new window)

Hjort, N. L. (1990). Nonparametric Bayes estimators based on Beta processes in models for life history data, Annals of Statistics, 18, 1259-1294. crossref(new window)

Jacod, J. and Shiryaev, A. N. (1987). Limit Theorems for Stochastic Processes, Springer, New York.

Kim, Y. (1999). Nonparametric Bayesian estimators for counting processes, Annals of Statistics, 27, 562-588. crossref(new window)

Kim, Y. (2001). Mixture of Beta processes for right censored data, Journal of the Korean Statistical Society, 30, 127-138.

Kim, Y. (2003). On posterior consistency of mixtures of Dirichlet processes with censored observations, Scandinavian Journal of Statistics, 30, 535-547. crossref(new window)

Kim, Y. and Hjort, N. (2012). Beta process envelopes around parametric models for survival analysis. Unpublished manuscript.

Kim, Y., James, L. and Weisbach, R. (2012). Bayesian analysis for multi-state event history data: The Beta-Dirichlet process prior, Biometrika.

Kim, Y. and Lee, J. (2001). On posterior consistency of survival models, Annals of Statistics, 29, 666-686. crossref(new window)

Kim, Y. and Lee, J. (2003). Bayesian analysis of proportional hazard models, Annals of Statistics, 31, 493-511. crossref(new window)

Kim, Y. and Lee, J. (2004). The Bernstein-von Mises theorem for survival models, Annals of Statistics, 32, 1492-1512. crossref(new window)

Kim, Y. (2006). The Bernstein-von Mises theorem of semiparametric Bayesian models for survival data, Annals of Statistics, 34, 1678-1700. crossref(new window)

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, (eds: Dey, D., Muller, P. and Sinha, D.).

Lee, J. and Kim, Y. (2004). A new algorithm to generate Beta processes, Computational Statistics and Data Analysis, 47, 441-453. crossref(new window)

Lo, A. Y. (1993). A Bayesian bootstrap for censored data, Annals of Statistics, 21, 100-123. crossref(new window)

Shen, X. and Wasserman, L. (2001). Rates of convergence of posterior distributions, Annals of Statistics, 29, 687-714. crossref(new window)

Susarla, V. and Van Ryzin, J. (1976). Nonparametric Bayesian estimation of survival curves from incomplete observations, Journal of the American Statistical Association, 71, 897-902. crossref(new window)

Walker, S. G. (2003). On sufficient conditions for Bayesian consistency, Biometrika, 90, 482-488. crossref(new window)

Walker, S. G. (2004). A new approach to Bayesian consistency, Annals of Statistics, 32, 2028-2043. crossref(new window)

Walker, S. and Hjort, N. L. (2001). On Bayesian consistency, Journal of the Royal Statistical Society, 63, 811-821. crossref(new window)

Walker, S. and Muliere, P. (1997). Beta-Stacy processes and a generalization of the Polya-urn scheme, Annals of Statistics, 25, 1762-1780. crossref(new window)

Wolpert, R.L. and Ickstadt K. (1998). Simulation of Levy random fields, In Practical Nonparametric and Semiparametric Bayesian Statistics, (eds. Dey, D., Muller, P. and Sinha, D.), 227-242.