Scalable Bayesian Inference for Bradley--Terry Models with Ties: An Application to Honour Based Abuse

TL;DR

This paper introduces an efficient Bayesian inference method for Bradley--Terry models with ties, applied to mapping honour-based abuse risks at community levels in the UK, addressing computational challenges in comparative judgment surveys.

Contribution

It develops a scalable MCMC algorithm for Bayesian Bradley--Terry models with ties, enabling detailed local-level abuse risk mapping from comparative data.

Findings

Mapped honour-based abuse risk in UK communities

Reduced survey fatigue through tied comparisons

Demonstrated computational efficiency of the new algorithm

Abstract

Honour based abuse covers a wide range of family abuse including female genital mutilation and forced marriage. Safeguarding professionals need to identify where abuses are happening in their local community to best support those at risk of these crimes and take preventative action. However, there is little local data about these kinds of crime. To tackle this problem, we ran comparative judgement surveys to map abuses at local level, where participants where shown pairs of wards and asked which had a higher rate of honour based abuse. In previous comparative judgement studies, participants reported fatigue associated with comparisons between areas with similar levels of abuse. Allowing for tied comparisons reduces fatigue, but increase the computational complexity when fitting the model. We designed an efficient Markov Chain Monte Carlo algorithm to fit a model with ties, allowing for a wide range of prior distributions on the model parameters. Working with South Yorkshire Police and Oxford Against Cutting, we mapped the risk of honour based abuse at community level in two counties in the UK.