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Urnings: A new method for tracking dynamically changing parameters in paired comparison systems
Bolsinova,Maria Maris,Gunter Hofman,Abe D. van der Maas,Han L. J. Brinkhuis,Matthieu J. S.
Bolsinova,Maria
Maris,Gunter
Hofman,Abe D.
van der Maas,Han L. J.
Brinkhuis,Matthieu J. S.
Abstract
We introduce a new rating system for tracking the development of parameters based on a stream of observations that can be viewed as paired comparisons. Rating systems are applied in competitive games, adaptive learning systems and platforms for product and service reviews. We model each observation as an outcome of a game of chance that depends on the parameters of interest (e.g. the outcome of a chess game depends on the abilities of the two players). Determining the probabilities of the different game outcomes is conceptualized as an urn problem, where a rating is represented by a probability (i.e. proportion of balls in the urn). This setup allows for evaluating the standard errors of the ratings and performing statistical inferences about the development of, and relations between, parameters. Theoretical properties of the system in terms of the invariant distributions of the ratings and their convergence are derived. The properties of the rating system are illustrated with simulated examples and its potential for answering research questions is illustrated using data from competitive chess, a movie review system, and an adaptive learning system for math.
Description
Funding information: The work of Maria Bolsinova was partially funded by the NAEd/Spencer Foundation Fellowship
Date
2022
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Keywords
paired comparisons, rating system, statistical inference, tracking
Citation
Bolsinova, M, Maris, G, Hofman, A D, van der Maas, H L J & Brinkhuis, M J S 2022, 'Urnings : A new method for tracking dynamically changing parameters in paired comparison systems', Journal of the Royal Statistical Society Series C-Applied Statistics, vol. 71, no. 1, pp. 91-118. https://doi.org/10.1111/rssc.12523