# Scalable Bayesian inference for bradley–Terry models with ties: an application to honour based abuse

## TL;DR

This paper introduces a scalable Bayesian method for analyzing honor-based abuse data using comparative judgment surveys, helping identify high-risk areas in local communities.

## Contribution

The paper presents an efficient MCMC algorithm for fitting Bradley-Terry models with ties, enabling scalable Bayesian inference for comparative judgment data.

## Key findings

- Allowing for tied comparisons in the model reduces participant fatigue in surveys.
- The proposed algorithm enables the use of a wide range of prior distributions for model parameters.
- The method was applied to map honor-based abuse risk in two UK counties.

## 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 the 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 the 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 the community level in two counties in the UK.