Prior probabilities are assigned at the SNP level and correspond to mutually exclusive events. We assigned a prior of for and , the probability that a SNP is associated with either of the two traits. Since all SNPs are assumed to have the same prior probability of association, this prior can be interpreted as an estimate for the proportion of SNPs that we expect to be associated with the trait in question. We also assigned a prior probability of for , the probability that one SNP is associated with both traits. This probability can be better understood when it is re-expressed as the conditional probability of a SNP being associated with trait 2, given that it is associated with trait 1. So assigning a probability of means that 1 in 100 SNPs that are associated with trait 1 is also associated with the other. As a sensitivity analysis, we ran the comparison with Teslovich et al. using two other prior probabilities for , which means 1 in 50 SNPs that are associated with one trait is also associated with the other; and which means 1 in 10 SNPs.
