SNP models. However, in large regions, a relatively modest number of SNPs can cause the number of three SNP models to be infeasible. For example, 100 SNPs can generate 4,950 two SNP models but 161,700 three SNP models. We would not suggest exploring four SNP models because that seems likely to spread the posterior probabilities very thinly, and we haven’t explored combining two and three SNP models because it is unclear what prior weight should be given to a two SNP compared to a three SNP model. As an example application of our proposed approaches, we analysed 13 loci associated with the autoimmune thyroid diseases GD and HT. Reassuringly, inference was broadly similar regardless of method, and we and showed that in the seven regions where a locus has been associated with the two diseases, the data are generally consistent with common causal variants exerting an equal effect on each disease. In regions previously significantly associated with only GD, posterior predictive p values are unlikely to detect any departure from colocalisation for reasons described above, but here the Bayesian approach does allow us to use make some inference using the posterior distribution of η . Given the relatively smaller number of HT cases (462) compared to GD (2285), it might be expected that many of the loci only associated with GD have failed to be reach significance for HT due to lack of power. Estimates of power to detect association with HT under the assumption of equal effects in GD and HT are broadly similar across the seven regions associated with both diseases and the six regions associated with GD only (Supplementary Table I), but these are likely to be over optimistic due to the expected bias in the GD effect size estimates. However, for five of these six regions, the evidence suggests that failure to detect association with HT is more likely to be due to a discrepancy in effect size, with the effect considerably larger in, and possibly specific to GD, compared to HT, rather than a lack of power. However, while the data suggest that LPP may have a stronger effect on GD compared to HT, and that CCR6 may be an undetected HT locus, the small sample size for HT prevents us from drawing this conclusion with any confidence. There is a pressing need for more widespread use of formal colocalisation testing. Researchers are turning to eQTL data to interpret GWAS results by simply considering whether an eQTL SNP is associated with any disease [Nicolae et al., 2010], visually [Trynka et al., 2011], by conditional testing [Nica et al., 2010], by naive application of a proportional colocalisation test [Plagnol et al., 2009; Wallace et al., 2012] or by attempting to integrate disease and gene expression association signals in networks [Hao et al., 2012]. Where colocalisation tests have been naively applied, we 17