Efficient Bayesian Inference for Generalized Bradley–Terry Models

@article{Caron2010EfficientBI,
  title={Efficient Bayesian Inference for Generalized Bradley–Terry Models},
  author={François Caron and A. Doucet},
  journal={Journal of Computational and Graphical Statistics},
  year={2010},
  volume={21},
  pages={174 - 196}
}
  • F. Caron, A. Doucet
  • Published 8 November 2010
  • Computer Science
  • Journal of Computational and Graphical Statistics
The Bradley–Terry model is a popular approach to describe probabilities of the possible outcomes when elements of a set are repeatedly compared with one another in pairs. It has found many applications including animal behavior, chess ranking, and multiclass classification. Numerous extensions of the basic model have also been proposed in the literature including models with ties, multiple comparisons, group comparisons, and random graphs. From a computational point of view, Hunter has proposed… 
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References

SHOWING 1-10 OF 48 REFERENCES
MM algorithms for generalized Bradley-Terry models
The Bradley-Terry model for paired comparisons is a simple and muchstudied means to describe the probabilities of the possible outcomes when individuals are judged against one another in pairs. Among
Generalized Bradley-Terry Models and Multi-Class Probability Estimates
TLDR
This paper introduces a generalized Bradley-Terry model in which paired individual comparisons are extended to paired team comparisons, and proposes a simple algorithm with convergence proofs to solve the model and obtain individual skill.
Bayesian inference for Plackett-Luce ranking models
TLDR
An efficient Bayesian method for inferring the parameters of a Plackett-Luce ranking model is given and a number of advantages of the EP approach over the traditional maximum likelihood method are shown.
A choice model with infinitely many latent features
TLDR
An MCMC algorithm for the EBA model is presented that can also be used in inference for other non-conjugate IBP models---this may broaden the use of IBP priors considerably.
A Matlab function to estimate choice model parameters from paired-comparison data
TLDR
A Matlab function is presented that makes it easy to specify any of these general models for paired-comparison data (EBA, Pretree, or BTL) and to estimate their parameters and eliminates the time-consuming task of constructing the likelihood function by hand for every single model.
Bayesian analysis of linear dominance hierarchies
Ties in Paired-Comparison Experiments: A Generalization of the Bradley-Terry Model
Abstract The Bradley-Terry model for a paired-comparison experiment with t treatments postulates a set of t ‘true’ treatment ratings π1, π2, · · ·, π t such that π i ≥ 0, ∑ π i = 1 and the
Gibbs sampling for Bayesian non‐conjugate and hierarchical models by using auxiliary variables
TLDR
The aim of the paper is to provide an alternative sampling algorithm to rejection‐based methods and other sampling approaches such as the Metropolis–Hastings algorithm.
Random graphs with a given degree sequence
Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is
An Exponential Family of Probability Distributions for Directed Graphs
TLDR
An exponential family of distributions that can be used for analyzing directed graph data is described, and several special cases are discussed along with some possible substantive interpretations.
...
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