small subset of models, and these models tend to contain sets of SNPs related by LD so that p $^{∗}$( m ) does not vary substantially across the set of models on which most of the posterior probability is concentrated. Whether caution is needed in applying this approach in smaller datasets depends somewhat on a researcher’s view. Certainly, it is unlikely that the ppp distribution would be uniform if small samples with weak associations were used, and therefore power to detect departure from colocalisation would be reduced. However, the alternative to colocalisation being tested is not just that of no colocalisation, but implicitly that of distinct causal variants in two traits. If there is weak or only limited evidence for association with either trait, then it does seem appropriate that one cannot reject a null of colocalising causal variants in favour of an alternative distinct causal variants. On the other hand, if evidence for association has been independently established, a researcher may be sure that there are causal variants for each trait although there is only weak evidence in the currently available datasets, in which case they may wish to explore calibrating the ppp distribution, for example by means of simulation [Hjort et al., 2006], so that its null distribution is uniform between [0 , 1]. Regions are typically defined after GWAS studies according to genetic distance in order to describe the physical region within which a causal variant tagged by the association is expected to lie. T1DBase uses a definition of 0.1cM surrounding any single SNP with p × 10 − 8 and we used a 0.1cM window around the most associated SNP in our AITD analysis. If regions were defined more broadly, one might expect the BMA method to be relatively unaffected, as SNPs beyond the boundary of the current regions would not show much evidence for association. On the other hand, we expect the power of the PC approach would decrease, as the number of components, and therefore the degrees of freedom of the test, would increase without any compensatory increase in information. We have proposed alternative approaches to colocalisation testing, but how should a researcher choose which approach and the parameters specific to that approach? Our view is that we would use PCs as a first pass if many loci are under consideration, to prioritise regions for more detailed analysis. The optimal number of components is unknown, but a number that captures something in the region of 70–90% of genetic variation seems acceptable. However, if evidence for association is strong in both datasets, BMA is a more powerful approach and there seems little reason beyond computational expense to prefer averaging over the universe of two SNP models to that of three 16