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Prior Distributions on Symmetric Groups

Published online by Cambridge University Press:  01 January 2025

Jayanti Gupta and
Paul Damien
Jayanti Gupta
Affiliation:
Merck Research Laboratories
Paul Damien*
Affiliation:
McCombs School of Business, University of Texas at Austin, TX
*
Requests for reprint should be sent to Paul Damien, McCombs School of Business, MSIS Dept. B6500, UT-Austin, Austin, TX 78712. E-mail: pdamien@bus.umich.ed
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Abstract

Fully and partially ranked data arise in a variety of contexts. From a Bayesian perspective, attention has focused on distance-based models; in particular, the Mallows model and extensions thereof. In this paper, a class of prior distributions, the Binary Tree, is developed on the symmetric group. The attractive features of the class are: it provides a closed-form solution to the posterior distribution; and a simple way to interpret the parameters of the prior distribution. The advantages of the proposed method are illustrated by comparing it to metric-based models using data analyzed by other researchers in this context.

Keywords

coset spacespermutation groupranked dataterminal sets

Information

Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 1 , March 2005, pp. 169 - 177
Copyright
Copyright © 2005 The Psychometric Society

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References

Critchlow, D.E. (1985). Metric Methods for Analyzing Partially Ranked Data. New York: Springer-Verlag.CrossRefGoogle Scholar
Critchlow, D.E., Fligner, M.A., & Verducci, J. (1991). Probability models on rankings. Journal of Mathematical Psychology, 35, 294–318.CrossRefGoogle Scholar
Diaconis, P. (1987). Group Representations in Probability and Statistics. Haywood, CA: Institute of Mathematical Statistics.Google Scholar
Diaconis, P. (1988). A generalization of spectral analysis with applications to ranked data. Annals of Statistics, 17, 949–979.Google Scholar
Ferguson, T.S. (1973). A Bayesian analysis of some nonparametric problems. Annals of Statistics, 1, 209–230.CrossRefGoogle Scholar
Fligner, M.A., & Verducci, J.S. (1986). Distance based ranking models. Journal of the Royal Statistical Society B, 48, 859–869.CrossRefGoogle Scholar
Fligner, M.A., & Verducci, J.S. (1988). Multistage ranking models. Journal of the American Statistical Association, 83, 892–901.CrossRefGoogle Scholar
Fligner, M.A., & Verducci, J.S. (1990). Posterior probabilities for a consensus ordering. Psychometrika, 55 (153–63.CrossRefGoogle Scholar
Lavine, M. (1992). Some aspects of Polya tree distributions for statistical modeling. Annals of Statistics, 20, 1203–1221.CrossRefGoogle Scholar
Mallows, C.L. (1957). Non null ranking models I. Biometrika, 44, 114–130.CrossRefGoogle Scholar
Thurstone, L.L. (1927). A law of comparative judgment. Psychological Reviews, 34, 273–286.CrossRefGoogle Scholar
Walker, S.G., Damien, P., Laud, P.W., & Smith, A.F.M. (1999). Bayesian nonparametric inference for random distributions and related functions (with discussion). Journal of the Royal Statistical Society B, 61, 485–527.CrossRefGoogle Scholar