Bayesian inference for partial orders underlying rank-data
Conference
65th ISI World Statistics Congress 2025
Format: IPS Abstract - WSC 2025
Keywords: "bayesian, "model"
Session: IPS 982 - PREFSTAT: Advanced Statistical Learning for Preference Rankings
Monday 6 October 10:50 a.m. - 12:30 p.m. (Europe/Amsterdam)
Abstract
When the underlying order constraining rank data is not a total order it is natural to allow the unknown order structure to be a partial order. Total orders, bucket orders and vertex-series-parallel orders are all partial orders but partial orders can represent more complex order relations. We give statistical methods for estimating partial orders from rank data. These models can be specified so that they contain well-known models for total orders, such as the Plackett Luce and Mallows models, as special cases. In our work on supervised learning from rank-order data, assessors provide preference orders over choice sets. The preferences of each assessor are represented as a partial order and we give a hierarchical model to correlate partial orders across assessors. The same setup can be used to group unlabelled rank data and uncover heterogeneity in the underlying partial orders across the sample population. In this session, I give Bayesian hierarchical models for partial orders and give examples of their use modelling social hierarchies and generic rank data.