Index: Caron 2012 - Bayesian Inference for Generalized Bradley-Terry Models

Caron 2012 - Bayesian Inference for Generalized Bradley-Terry Models

Routing Summary

Full capture of Caron & Doucet (JCGS 2012; INRIA RR-7445 / arXiv:1011.1761): EM and Gamma-Gibbs algorithms for Bradley-Terry, home advantage, ties, team comparisons and Plackett-Luce, plus identifiability, hyperparameters and experiments. 6 notes.

• Need the paper on one page or the section-to-note map? → Caron 2012 - Bayesian Inference for Generalized Bradley-Terry Models - Overview
• Need the BT likelihood, latent Gamma variable, EM/MM and Gibbs updates? → Caron 2012 - Bradley-Terry Likelihood and Latent Exponential Augmentation
• Need home advantage, Rao-Kupper ties, or team comparisons? → Caron 2012 - Home Advantage, Ties and Team Comparisons
• Need Plackett-Luce for full rankings? → Caron 2012 - Plackett-Luce Model for Full Rankings
• Need identifiability, rescaling, learning the prior shape, random graphs, Tversky choice? → Caron 2012 - Identifiability, Hyperparameters and Further Extensions
• Need NASCAR/chess results and Table 1? → Caron 2012 - Experiments NASCAR and Chess

Concept Map

Concept	Note	Type	Depends On	Key Result
BT log-likelihood, latent Gamma $Z_{ij}$	Caron 2012 - Bradley-Terry Likelihood and Latent Exponential Augmentation	theorem	Overview	MM = EM; Gamma Gibbs
Home advantage $\theta$	Caron 2012 - Home Advantage, Ties and Team Comparisons	theorem	BT	$\theta \sim$ Gamma conditional
Rao-Kupper ties	Caron 2012 - Home Advantage, Ties and Team Comparisons	theorem	BT	$\theta$ conditional is a Gamma mixture
Team BT	Caron 2012 - Home Advantage, Ties and Team Comparisons	theorem	BT	winner-id latent $C_i$
Plackett-Luce	Caron 2012 - Plackett-Luce Model for Full Rankings	theorem	BT	stage-wise exponentials
Dirichlet-Gamma identifiability	Caron 2012 - Identifiability, Hyperparameters and Further Extensions	theorem	BT	only $\pi$ identified; rescale step
NASCAR / chess	Caron 2012 - Experiments NASCAR and Chess	example	all	Gibbs beats M-H; Bayes beats MAP

Notes

• Caron 2012 - Bayesian Inference for Generalized Bradley-Terry Models - Overview — CONTAINS: contributions, model table, Source Map, PyMC example link.
• Caron 2012 - Bradley-Terry Likelihood and Latent Exponential Augmentation — CONTAINS: Def. BT, latent $Z$; Thm. EM and Gibbs; toy tournament; Python/PyMC.
• Caron 2012 - Home Advantage, Ties and Team Comparisons — CONTAINS: Sec. 3.1-3.3 definitions and algorithms.
• Caron 2012 - Plackett-Luce Model for Full Rankings — CONTAINS: PL likelihood, latents, EM/Gibbs, creative-ranking example, Python.
• Caron 2012 - Identifiability, Hyperparameters and Further Extensions — CONTAINS: Sec. 5.
• Caron 2012 - Experiments NASCAR and Chess — CONTAINS: Sec. 6-7, Table 1.

Sources

Caron and Doucet 2012 - Efficient Bayesian Inference for Generalized Bradley-Terry Models

See Also

Discrete Choice Models · Reward Modeling from Human Preferences · Hierarchical Models