Efficient Bayesian inference for generalized Bradley-Terry models

Journal of Computational and Graphical Statistics

Volumn 21, Issue 1, 2012, Pages 174-196

  Caron, François ^a   Doucet, Arnaud ^b  

^a UNIVERSITÉ BORDEAUX 1   (France)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Data augmentation; EM algorithm; Gibbs sampler; Maximum likelihood estimation; MCMC algorithms; MM algorithm; Plackett Luce model; Rank data

Indexed keywords

EID: 84859870166     PISSN: 10618600     EISSN: None     Source Type: Journal    
DOI: 10.1080/10618600.2012.638220     Document Type: Article

References (32)

1. Adams, E. (2005), "Bayesian Analysis of Linear Dominance Hierarchies, " Animal Behaviour, 69, 1191-1201.[175]
2. Agresti, A. (1990), Categorical Data Analysis, New York: Wiley.[175, 178, 189]
3. Barndorff-Nielsen, O., and Shephard, N. (2001), "Non-Gaussian Ornstein-Uhlenbeck-Based Models and Some of Their Uses in Financial Economics, " Journal of the Royal Statistical Society, Series B, 63, 167-241.[188]
4. Bradley, R., and Terry, M. (1952), "Rank Analysis of Incomplete Block Designs. I. The Method of Paired Comparisons, " Biometrika, 39, 324-345.[174]
5. Chatterjee, S., Diaconis, P., and Sly, A. (2010), "Random Graphs With a Given Degree Sequence, " Technical Report, Stanford University.[187]
6. Damien, P., Wakefield, J., and Walker, S. (1999), "Gibbs Sampling for Bayesian Non-Conjugate and Hierarchical Models by Using Auxiliary Variables," Journal of the Royal Statistical Society, Series B, 61, 331-344.[187]
7. David, H. (1988), The Method of Paired Comparisons, Oxford: Oxford University Press.[175]
8. Davidson, R., and Farquhar, P. (1976), "A Bibliography on the Method of Paired Comparisons, " Biometrics, 32, 241-252.[175]
9. Diaconis, P. (1988), "Group Representations in Probability and Statistics, " IMS Lecture Notes, (vol. 11), Beachwood, OH: Institute of Mathematical Statistics.[175, 175, 176]
10. Elo, A. (1978), The Rating of Chess Players, Past and Present, New York: Arco Pub.[193]
11. Glickman, M. (1995), "A Comprehensive Guide to Chess Ratings, " Technical Report, Boston University, Department of Statistics.[193]
12. Gormley, I., and Murphy, T. (2008), "Exploring Voting Blocs With the Irish Electorate: A Mixture Modeling Approach, " Journal of the American Statistical Association, 103, 1014-1027.[185]
13. Gormley, I., and Murphy, T. (2009), "A Grade of Membership Model for Rank Data, " Bayesian Analysis, 4, 265-296.[175, 177, 189, 190]
14. G̈or̈ur, D., J̈akel, F., and Rasmussen, C. (2006), "A Choice Model With Infinitely Many Latent Features, " in Proceedings of the 23rd International Conference on Machine Learning, Pittsburgh, PA, pp. 361-368.[189]
15. Guiver, J., and Snelson, E. (2009), "Bayesian Inference for Plackett-Luce Ranking Models, " in Proceedings of the 26th Annual International Conference on Machine Learning, New York, NY, pp. 377-384.[175, 177]
16. Hastie, T., and Tibshirani, R. (1998), "Classification by Pairwise Coupling, " The Annals of Statistics, 26, 451-471.[175]
17. Holland, P., and Leinhardt, S. (1981), "An Exponential Family of Probability Distributions for Directed Graphs, " Journal of the American Statistical Association, 76, 33-65.[187]
18. Huang, T.-K., Weng, R., and Lin, C.-J. (2006), "Generalized Bradley-Terry Models and Multi-Class Probability Estimates, " Journal of Machine Learning Research, 7, 85-115.[175, 182]
19. Hunter, D. (2004), "MM Algorithms for Generalized Bradley-Terry Models, " The Annals of Statistics, 32, 384-406.[174, 175, 176, 178, 179, 181, 184, 190, 194]
20. Lange, K., Hunter, D., and Yang, I. (2000), "Optimization Transfer Using Surrogate Objective Functions" (with discussion), Journal of Computational and Graphical Statistics, 9, 1-59.[175]
21. Liu, J. (2001), Monte Carlo Methods for Scientific Computing, New York: Springer-Verlag.[177]
22. Luce, R. (1959), Individual Choice Behavior: A Theoretical Analysis, New York: Wiley.[175, 176, 184]
23. Luce, R. (1977), "The Choice Axiom After Twenty Years," Journal of Mathematical Psychology, 15, 215- 233.[175]
24. Meng, X.-L., and Rubin, D. (1993), "Maximum Likelihood Estimation via the ECM Algorithm: A General Framework, " Biometrika, 80, 267-278.[179]
25. Park, J., and Newman, M. (2004), "The Statistical Mechanics of Networks, " Physical Review E, 70, 066117.[187]
26. Plackett, R. (1975), "The Analysis of Permutations, " Applied Statistics, 24, 193-202.[175, 176, 184]
27. Rao, P., and Kupper, L. (1967), "Ties in Paired-Comparison Experiments: A Generalization of the Bradley-Terry Model, " Journal of the American Statistical Association, 62, 194-204.[175, 180]
28. Restle, F. (1961), Psychology of Judgement and Choice, New-York: Wiley.[189]
29. Tversky, A. (1972a), "Choice by Elimination, " Journal of Mathematical Psychology, 9, 341-367.[189]
30. Tversky, A. (1972b), "Elimination by Aspects: A Theory of Choice, " Psychological Review, 79, 281-299.[189]
31. Wickelmaier, F., and Schmid, C. (2004), "A Matlab Function to Estimate Choice Model Parameters From Paired- Comparison Data, " Behavior Research Methods, Instruments and Computers, 36, 29-40.[189]
32. Zermelo, E. (1929), "Die berechnung der turnier-ergebnisse als ein maximumproblem der wahrscheinlichkeitsrechnung, " Mathematische Zeitschrift, 29, 436-460.[175]