Abstract
Comparative judgement studies elicit quality assessments through pairwise comparisons, typically analysed using the Bradley–Terry model. We have developed a suite of spatial comparative judgement models and run studies to map the prevalence of crimes such as domestic abuse, modern slavery, and forced marriage. This talk describes work on extracting more information per comparison, organised around three extensions to the standard model. First, a multivariate normal prior distribution whose covariance matrix is built from the network of areas in the study. This lets neighbouring areas borrow strength and reduces the data required by around ninety per cent. Second, a Pólya-Gamma latent variable representation that yields a Gaussian full conditional while retaining that correlated prior distribution, which allows inference to be carried out in 20 to 30 seconds. Third, an experimental design that weights pairs by the prior variance they explain, made computable for large studies by a reduced basis decomposition of the associated pairs-of-pairs covariance matrix. We demonstrate these methods in several real world studies, describe the changes they have brought about in safeguarding practice, and outline our steps towards commercialising the work.