distribution and compute Bayesian posteriors12; data can be combined across multiple ancestry reference panels to further boost accuracy17,18. Singular value decomposition based approaches for LD regularization have also been proposed in other contexts10. In general, the accuracy of conditional association and imputation using summary statistics is reduced at low-frequency variants and when the LD structure between typed and imputed SNPs is mis-specified (e.g., when the ancestry of the GWAS sample does not exactly match the reference panel). We note that concerns about false-positive associations in imputation using summary statistics can be avoided entirely via the release of in-sample summary LD information, i.e. pairwise correlations between all typed SNPs.
