# Modelling Preference Data with the Wallenius Distribution

## TL;DR

This paper introduces a Bayesian computational method for modeling categorical preference data using the Wallenius distribution, enabling classification and analysis of ranking preferences in various datasets.

## Contribution

The paper develops an ABC-based estimation approach for the Wallenius distribution and applies it to real and simulated data, including a novel dataset on statisticians' journal preferences.

## Key findings

- Effective estimation of category importance using ABC
- Successful application to movie ratings data
- Novel analysis of statisticians' journal preferences

## Abstract

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 about movies ratings and Italian academic statisticians' journal preferences. The latter is a novel dataset collected by the authors.