The utility of the Laplace effect size prior distribution in Bayesian fine‐mapping studies

Abstract

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.

Probabilistic identification of bacterial essential genes via insertion density using TraDIS data with Tn5 libraries

“…We assume that there is no cost in making the correct decision. There are, therefore, two costs to assign: false discovery cost ( C A ) when INSDENS incorrectly identifies a gene as essential when it is actually non-essential and the false non-discovery cost ( C B ) when INSDENS identifies a gene as non-essential when it is actually essential ( Walters et al , 2021 ). Bayesian decision theory states that gene i is declared to be essential if the posterior cost of declaring it to be essential is less than the posterior cost of declaring it be non-essential.…”

Methods for statistical fine-mapping and their applications to auto-immune diseases

“…Similarly, harmonizing heterogeneous datasets with different underlying technologies (such as different arrays, whole exome, or genome sequencing) and including low-frequency variants is thought to be fruitful for further discovery of putative causal variants underlying human complex disorders by increasing the statistical power and the coverage of the genome. Another direction is the optimization of the prior distribution of the causal effect sizes [83,84] (not the causal configuration); for example, Walters et al [83] suggested Laplace prior could increase the statistical power compared to the commonly used normal distribution. As optimizing the prior is a non-trivial problem in Bayesian analysis in general, it could be also valuable to discuss the possibility of moving outside of the Bayesian world to practice statistical fine-mapping in a frequentist approach.…”

Bayesian multivariant fine mapping using the Laplace prior

“…We provide the SNP number from 1 to 1733 (rather than 1 to 90) for the top 10 ranked SNPs. This is for ease of comparison with Walters et al (2021). The prior probabilities of the number of causal SNPs used in this analysis are provided in Table 2.…”

“…The Gaussian distribution is not the only distribution that has been considered for the effect size prior in univariate analyses. The t distribution (Marchini & Howie, 2010), the normal‐gamma distribution (Alenazi et al, 2019; Boggis et al, 2016) and the Laplace distribution (Hoggart et al, 2008; Walters et al, 2021) have all been considered. Walters et al (2019) assessed the fit of the Gaussian and Laplace priors using Bayesian model selection.…”

“…They analysed the estimated effect sizes of a large number of independent breast cancer genome‐wide association study (GWAS) top hits and found that the Laplace prior gave a higher model posterior probability than the Gaussian prior. Following on from the findings of Walters et al (2019), Walters et al (2021) explored the performance of the Laplace prior (compared to the Gaussian prior) in Bayesian fine mapping. They only considered univariate analyses and examined the causal SNP ranks via receiver‐operating characteristic (ROC) curves and credible set sizes.…”