if available, or approximated using an appropriate reference panel such as the 1000 Genomes. We obtain annotations from external repositories (e.g. ENCODE [18]) and for each SNP , create a -length binary annotation vector , where if the SNP at the locus is part of annotation . For example, one such annotation could be all coding sites and the annotation vector will contain a 1 only if the SNP is located within coding region. We note that and serves to represent the “baseline” annotation whose corresponding coefficient can be interpreted as the baseline prior odds for causality of any SNP within the set of fine-mapping loci. Let be the effect size of the annotation on the probability of a SNP being causal and the non-centrality parameter, , be the standardized effect size of SNP at locus . Finally, let be an indicator vector of causality where if SNP at locus is causal and 0 otherwise. Now, we can define the likelihood of the data relative to these terms as:(1)where the sum is taken across all causal indicator vector sets . We note that in order to keep the enumeration of the causal vector sets combinatorially tractable, we restrict the total
