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Title: Rating with the pairwise empirical Bayes method Authors:  Cristiano Varin - Ca Foscari University of Venice (Italy) [presenting]
David Firth - University of Warwick (United Kingdom)
Abstract: The problem of rating $q$ subjects or items on the basis of a set of $n$ paired comparisons is considered. This problem frequently arises in a variety of fields including psychometrics, analysis of sport tournaments and genetics. Standard analysis of paired comparison data based on Bradley-Terry and Thurstone-Mosteller models becomes difficult in case of sparse tournaments where only a small fraction of all possible paired comparisons is observed. In such situations, empirical Bayes estimation is attractive because it allows borrowing strength across the subjects abilities. Empirical Bayes estimation is numerically impractical in paired comparison models involving a large number of subjects $q$, because the evaluation of the joint marginal distribution of the data requires approximating intractable $q$-dimensional integrals. We shall discuss an approach to overcome the numerical difficulties associated with the evaluation of the marginal likelihood through a combination of composite likelihood and empirical Bayes methods.