Abstract
Modeling and analysis of ranks have received renewed interest in the era of big data, when recruited and volunteer assessors compare and rank objects to facilitate decision making in disparate areas, from politics to entertainment, from education to marketing. In the field of genomics, use of ranks has been advocated because of its platform independence, and has been successful for prediction models and for meta analysis. The Mallows rank model is among the most successful approaches, but its use has been limited to a particular form based on the Kendall distance, for which the normalizing constant has a simple analytic expression. In the work presented, we develop computationally tractable methods for performing Bayesian inference in Mallows models with any right-invariant metric, thereby allowing for greatly extended flexibility. Our methods also allow estimation of consensus rankings for data in the form of top-t rankings, pairwise comparisons, and other linear orderings. In addition, clustering via mixtures allows finding substructure among assessors. Finally we construct a regression framework for ranks which vary over time. We illustrate and investigate our approach on simulated data, on performed experiments, and on benchmark data.
Reference
Sørensen Ø, Vitelli V, Frigessi A, and Arjas E. 2014; arXiv: 1405.7945,