Although it is difficult to derive E(βb|β^b,D^b) from the joint conditional distribution of βb, each element of βb follows a mixed normal distribution conditioning on β^b, D^b, and all other elements in βb. Therefore, we apply a Gibbs sampler to draw samples from f(βb|β^b,D^b) and use the sample mean as an approximation for E(βb|β^b,D^b). We further performed a sensitivity analysis on the choice of the size of block b (S6 Fig). Specifically, we ran AnnoPred on the data of Crohn’s disease with different sizes of block and found that the results were robust to the sizes. In practice, the size of block b is specified by the total number of variants divided by 3,000.
