Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

Bayesian Multiple Comparisons for Normal Variances

  • Published : 2000.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

Regarding to multiple comparison problem (MCP) of k normal population variances, we suggest a Bayesian method for calculating posterior probabilities for various hypotheses of equality among population variances. This leads to a simple method for obtaining pairwise comparisons of variances in a statistical experiment with a partition on the parameter space induced by equality and inequality relationships among the variances. The method is derived from the fact that certain features of the hierarchical nonparametric family of Dirichlet process priors, in general, make it amenable to solving the MCP and estimating the posterior probabilities by means of posterior simulation, the Gibbs sampling. Two examples are illustrated for the method. For these examples, the method is straightforward for specifying distributionally and to implement computationally, with output readily adapted for required comparison.

Keywords

References

  1. The Annals of Statistics v.2 Mixtures of Dirichlet processes with application to Bayesian nonparametric problems Antoniak, C.E.
  2. Bayesian Statistics v.3 Multiple comparisons, multiple tests and data dredging;a Bayesian perspective Berry, D.A.;Bernardo, J.M.(ed.)
  3. Journal of the American Statistical Association v.92 Testing and locating variance change points with application to stock prices Chen, J.;Gupta, A.K.
  4. Journal of the American Statistical Association v.91 Markov chain Monte Carlo convergence diagnostics;a comparative review Cowles, M.K.;Carlin, B.P.
  5. Journal of the American Statistical Association v.90 Bayesian density estimation and inferences using mixtures Escorbar, M.D.;West, M.
  6. The Annals of Statistics v.1 A Bayesian analysis of some nonparametric problems Ferguson, T.S.
  7. Journal of the American Statistical Association v.93 Bayesian multiple comparisons using Dirichlet process prior Gopalan, R.;Berry, D.A.
  8. Multiple Comparison Procedures Hochberg, T.;Tambane, A.C.
  9. Applied Statistics v.26 Tests of variance shifts at an unknown time point Hsu, D.A.
  10. Journal of Business and Economic Statistics v.11 Detection of multiple changes of variance using posterior odds Inclan, C.
  11. The Annals of Statistics v.24 Nonparametric hierarchical Bayes via sequential imputations Liu, J.
  12. Journal of Computational and Graphical Statistics v.7 Estimating mixture Dirichlet process models MacEachern, S.N.;Muller, P.
  13. Soviet Mathematics Doklady v.24 Detecting disorder in multidimensional random processes Vostrikova, L.J.