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Modelling preference data with the Wallenius distribution
Author(s) -
Grazian Clara,
Leisen Fabrizio,
Liseo Brunero
Publication year - 2019
Publication title -
journal of the royal statistical society: series a (statistics in society)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.103
H-Index - 84
eISSN - 1467-985X
pISSN - 0964-1998
DOI - 10.1111/rssa.12415
Subject(s) - generalization , hypergeometric distribution , ranking (information retrieval) , preference , data set , set (abstract data type) , computer science , bayesian probability , distribution (mathematics) , mathematics , artificial intelligence , statistics , mathematical analysis , programming language
Summary The Wallenius distribution is a generalization of the hypergeometric distribution where weights are assigned to balls of different colours. This naturally defines a model for ranking categories which can be used for classification. Since, in general, the resulting likelihood is not analytically available, we adopt an approximate Bayesian computational approach for estimating the importance of the categories. We illustrate the performance of the estimation procedure on simulated data sets. Finally, we use the new model for analysing two data sets concerning movie ratings and Italian academic statisticians’ journal preferences. The latter is a novel data set collected by the authors.