These approaches reduce the dimensionality of the inference while modelling the complete data, rather than summarising each gene before combining evidence. These methods offer promise for genome-wide association scans, an important open question being the precision in estimating the random effects distribution when the number and size of true associations are small. For example, a method for testing whether the overall distribution of p-values is uniform[39] has very little power compared with the Bonferroni correction when the number of true effects is small (authors' unpublished data). Another important issue is the choice of random effects distribution: current methods assume hierarchical or mixture normal distributions, but experimental geneticists have favoured gamma distributions [40,41]. A useful feature of the mixture distribution models is that they generate maximumlikelihood probabilities of membership to each of the mixture components, for each gene, which can be interpreted informally as posterior probabilities of association allowing individual genes to be selected for follow-up study.
