Although we have not encountered any dataset where FINEMAP would not have performed well, theoretically, it remains possible that an in-exhaustive search could miss some relevant causal configurations. A simple way to assess possible problems is to run many searches in parallel and compare and combine their outcomes. Another way is parallel tempering (Geyer, 1991) where several searches are run in parallel in different ‘temperatures’. Intuitively, increasing temperature flattens the likelihood function and hence a search in a higher temperature moves around more freely than one in a colder temperature. Such an approach, together with complex global transition mechanisms to escape from local modes, was introduced in an evolutionary stochastic search algorithm by Bottolo and Richardson (2010) that was later tailored for genetic analyses of multiple SNPs and multivariate phenotypes in the software package GUESS (Bottolo et al., 2013). These two papers could give ideas how FINEMAP could be further modified if trapping into local modes of the search space were encountered in real data analyses of GWAS regions.
