The default causal single-nucleotide polymorphism (SNP) effect size prior in Bayesian fine-mapping studies is usually the Normal distribution. This choice is often based on computational convenience, rather than evidence that it is the most suitable prior distribution. The choice of prior is important because previous studies have shown considerable sensitivity of causal SNP Bayes factors to the form of the prior. In some well-studied diseases there are now considerable numbers of genome-wide association study (GWAS) top hits along with estimates of the number of yet-to-be-discovered causal SNPs. We show how the effect sizes of the top hits and estimates of the number of yet-to-bediscovered causal SNPs can be used to choose between the Laplace and Normal priors, to estimate the prior parameters and to quantify the uncertainty in this estimation. The methodology can readily be applied to other priors. We show that the top hits available from breast cancer GWAS provide overwhelming support for the Laplace over the Normal prior, which has important consequences for variant prioritisation. This work in this paper enables practitioners to derive more objective priors than are currently being used and could lead to prioritisation of different variants. K E Y W O R D SBayesian, fine-mapping, Laplace, normal, prior

The Gaussian distribution is usually the default causal single-nucleotide polymorphism (SNP) effect size prior in Bayesian population-based finemapping association studies, but a recent study showed that the heavier-tailed Laplace prior distribution provided a better fit to breast cancer top hits identified in genome-wide association studies. We investigate the utility of the Laplace prior as an effect size prior in univariate fine-mapping studies. We consider ranking SNPs using Bayes factors and other summaries of the effect size posterior distribution, the effect of prior choice on credible set size based on the posterior probability of causality, and on the noteworthiness of SNPs in univariate analyses. Across a wide range of fine-mapping scenarios the Laplace prior generally leads to larger 90% credible sets than the Gaussian prior. These larger credible sets for the Laplace prior are due to relatively high prior mass around zero which can yield many noncausal SNPs with relatively large Bayes factors. If using conventional credible sets, the Gaussian prior generally yields a better trade off between including the causal SNP with high probability and keeping the set size reasonable. Interestingly when using the less well utilised measure of noteworthiness, the Laplace prior performs well, leading to causal SNPs being declared noteworthy with high probability, whilst generally declaring fewer than 5% of noncausal SNPs as being noteworthy. In contrast, the Gaussian prior leads to the causal SNP being declared noteworthy with very low probability.

Currently, the only effect size prior that is routinely implemented in a Bayesian fine‐mapping multi‐single‐nucleotide polymorphism (SNP) analysis is the Gaussian prior. Here, we show how the Laplace prior can be deployed in Bayesian multi‐SNP fine mapping studies. We compare the ranking performance of the posterior inclusion probability (PIP) using a Laplace prior with the ranking performance of the corresponding Gaussian prior and FINEMAP. Our results indicate that, for the simulation scenarios we consider here, the Laplace prior can lead to higher PIPs than either the Gaussian prior or FINEMAP, particularly for moderately sized fine‐mapping studies. The Laplace prior also appears to have better worst‐case scenario properties. We reanalyse the iCOGS case–control data from the CASP8 region on Chromosome 2. Even though this study has a total sample size of nearly 90,000 individuals, there are still some differences in the top few ranked SNPs if the Laplace prior is used rather than the Gaussian prior. R code to implement the Laplace (and Gaussian) prior is available at https://github.com/Kevin-walters/lapmapr.