Modelling Preference Data with the Wallenius Distribution

The Wallenius distribution is a generalisation 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 purposes. Since, in general, the resulting likelihood is not analytically available, we adopt an approximate Bayesian

computational (ABC) approach for estimating the importance of the categories. We illustrate the performance of the estimation procedure on simulated datasets. Finally,

we use the new model for analysing two datasets concerning movies ratings and Italian academic statisticians' journal preferences. The latter is a novel dataset collected by

the authors.