Some Issues in Bayesian Nonparametrics

  • Ronald C. Pruitt
Conference paper


The field of Bayesian nonparametrics encompasses ideas of both a foundational and technical nature. There are no unifying concepts, although the Dirichlet process and related ideas have become very popular. Here we illustrate some of the issues, and in some cases how computational ability has changed them.

The talk will address two questions. The first is: Why bother with Bayesian nonparametrics? We argue that it is a sensible intermediate between an analysis based on complete ignorance and one based on very specific knowledge. Problems where Bayesian nonparametric and computer-intensive techniques are applicable will be illustrated. Each has strengths for different types of problems.

The second question is: Why is the Dirichlet process so popular, and should it be? The Dirichlet process has many appealing features as a nonparametric prior, but it also has some shortcomings. Among undesirable features, we will discuss some aspects of the limited flexibility allowed to express prior opinion and a new inconsistency example which arises with bivariate censored data.


Bayesian Inference Dirichlet Process Generalize Maximum Likelihood Survival Curve Analysis Bayesian Robustness 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    ANTONIAK, C.E. (1974). Mixtures of Dirichlet processes with applications to Bayesian nonparametric problems. Ann. Statist. 2 1152–1174.MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    BERGER, J. (1984). The robust Bayesian viewpoint. In Robustness of Bayesian analysis. J.B. Radane, ed. North-Holland, 63–144.Google Scholar
  3. [3]
    BOSE, S. (1990). Bayesian Robustness with Mixture Priors and Shape-constrained Priors. Ph.D. thesis, Purdue University.Google Scholar
  4. [4]
    DEROBERTIS, L. and HARTIGAN, J. (1981). Bayesian inference using intervals of measures. Ann. Statist. 9 235–244.MathSciNetCrossRefGoogle Scholar
  5. [5]
    DIACONIS, P., and FREEDMAN, D. (1986a). On the consistency of Bayes estimates. Ann. Statist 14 1–26.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    DIACONIS, P., and FREEDMAN, D. (1986b). On inconsistent Bayes estimates of location. Ann. Statist 14 68–87.MathSciNetMATHCrossRefGoogle Scholar
  7. [7]
    DOSS, H. (1985a). Bayesian nonparametric estimation of the median; part I: Computation of the estimates. Ann. Statist. 13 1432–1444.MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    DOSS, H. (1985b). Bayesian nonparametric estimation of the median; part II: Asymptotic properties of the estimates. Ann. Statist 13 1445–1464.MathSciNetMATHCrossRefGoogle Scholar
  9. [9]
    FERGUSON, T.S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist 1 209–230.MathSciNetMATHCrossRefGoogle Scholar
  10. [10]
    FERGUSON, T.S., PHADIA, E.G. and TIWARI, R.C (1989). Bayesian nonparametric inference. Preprint Google Scholar
  11. [11]
    HILL, B. (1968). Posterior distribution of percentiles: Bayes theorem for sampling from a finite population. J. Amer. Statist Assoc. 63 677–691.MathSciNetMATHCrossRefGoogle Scholar
  12. [12]
    KUO, L. (1986). Computations of mixtures of Dirichlet processes. SIAM J. Sci. Statist Comput 7 60–71.MathSciNetCrossRefGoogle Scholar
  13. [13]
    LAVINE, M. (1987). Prior influence in Bayesian statistics. Ph.D. thesis, University of Minnesota.Google Scholar
  14. [14]
    LO, A. (1984). On a class of Bayesian non-parametric estimates: I. Density estimates. Ann. Statist. 12 351–357.MathSciNetMATHCrossRefGoogle Scholar
  15. [15]
    MARSHALL, A.W. and OLKIN, I. (1988). Families of multivariate distributions. J. Amer. Statist. Assoc. 83 834–841.MathSciNetMATHCrossRefGoogle Scholar
  16. [16]
    PRUITT, R. (1988). Bayesian survival curve estimation for incompletely observed multivariate data. Preprint. University of Minnesota.Google Scholar
  17. [17]
    PRUITT, R. (1989). An inconsistent Bayes estimator in bivariate survival curve analysis. Technical Report 529, University of Minnesota.Google Scholar
  18. [18]
    PRUITT, R. (1991a). Smoothing the generalized maximum likelihood estimator for bivariate survival data. In preparation. University of Minnesota.Google Scholar
  19. [19]
    PRUITT, R. (1991b). Small sample comparison of five bivariate survival curve estimators. In preparation. University of Minnesota.Google Scholar
  20. [20]
    WEST, M. (1990). Bayesian kernel density estimation. Preprint, Duke University.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1992

Authors and Affiliations

  • Ronald C. Pruitt
    • 1
  1. 1.University of Minnesota School of StatisticsUniversity of MinnesotaMinneapolisUSA

Personalised recommendations