A Bayesian nonparametric approach for generalized Bradley-Terry models in random environment
| Autor: | Le Corff, Sylvain, Lerasle, Matthieu, Vernet, Elodie |
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| Přispěvatelé: | Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques d'Orsay (LM-Orsay), Model selection in statistical learning (SELECT), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria) |
| Rok vydání: | 2018 |
| Předmět: |
Methodology (stat.ME)
FOS: Computer and information sciences ComputingMethodologies_PATTERNRECOGNITION [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] FOS: Mathematics Mathematics - Statistics Theory [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH] Statistics Theory (math.ST) [STAT.ME]Statistics [stat]/Methodology [stat.ME] Statistics - Methodology |
| DOI: | 10.48550/arxiv.1808.08104 |
| Popis: | This paper deals with the estimation of the unknown distribution of hidden random variables from the observation of pairwise comparisons between these variables. This problem is inspired by recent developments on Bradley-Terry models in random environment since this framework happens to be relevant to predict for instance the issue of a championship from the observation of a few contests per team. This paper provides three contributions on a Bayesian nonparametric approach to solve this problem. First, we establish contraction rates of the posterior distribution. We also propose a Markov Chain Monte Carlo algorithm to approximately sample from this posterior distribution inspired from a recent Bayesian nonparametric method for hidden Markov models. Finally, the performance of this algorithm are appreciated by comparing predictions on the issue of a championship based on the actual values of the teams and those obtained by sampling from the estimated posterior distribution. |
| Databáze: | OpenAIRE |
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