Abstract
Within the context of non-parametric Bayesian inference, Dykstra and Laud (1981) define an extended gamma (EG) process and use it as a prior on increasing hazard rates. The attractive features of the extended gamma (EG) process, among them its capability to index distribution functions that are absolutely continuous, are offset by the intractable nature of the computation that needs to be performed. Sampling based approaches such as the Gibbs Sampler can alleviate these difficulties but the EG processes then give rise to the problem of efficient random variate generation from a class of distributions called D-distributions. In this paper, we describe a novel technique for sampling from such distributions, thereby providing an efficient computation procedure for non-parametric Bayesian inference with a rich class of priors for hazard rates.
This is a preview of subscription content, access via your institution.
References
Antoniak, C. E. (1974) Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Annals of Statistics, 2, 1152–1174.
Devroye, L. (1986) Non-Uniform Random Variate Generation. Springer-Verlag, New York.
Doksum, K. A. (1974) Tailfree and neutral random probabilities and their posterior distributions. Annals of Probability, 2, 183–201.
Dykstra, R. L. and Laud, P. W. (1981) A Bayesian nonparametric approach to reliability. Annals of Statistics, 9, 356–367.
Ferguson, T. S. (1973) A Bayesian analysis of some nonparametric problems. Annals of Statistics, 1, 209–230.
Ferguson, T. S. and Phadia, E. G. (1979) Bayesian nonparametric estimation based on censored data. Annals of Statistics, 7, 163–186.
Gelfand, A. E. and Smith, A. F. M. (1990) Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398–409.
Gilks, W. and Wild, R. (1992) Adaptive rejection sampling for Gibbs sampling. Applied Statistics, 41, 337–348.
Laud, P. W. (1977) Bayesian nonparametric inference in reliability. Ph.D. Dissertation, University of Missouri, Columbia, MO.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Laud, P.W., Ramgopal, P. & Smith, A.F.M. Random variate generation from D-distributions. Stat Comput 3, 109–112 (1993). https://doi.org/10.1007/BF00147773
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00147773
Keywords
- Extended gamma process (EG)
- D-distributions
- truncated density
- rejection
- algorithm