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## G Additional simulations for the two-samples prob- lem 

Table 6 shows a comparison of the performance of the minimum p -value and Fisher- combined test statistics. The variant with highest power in most setups (specifically, setups 2,4,5,6,8,9,10,11,12) is the Fisher-combined p -value using aggregation by sum- mation and m$_{max}$ = 50. However, the Fisher-combined p -value test is sensitive to the choice of m$_{max}$ , which is unknown in practice. Since we view this as a significant weakness of the Fisher-combined statistic, and since the minimum p -value does not have this weakness and has very good power when compared with Fisher as well as when compared with other tests (with a large range of m$_{max}$ values examined), we recommend the minimum p -value test statistic. 

<img src='content_image/319092.jpg'>

Table 7 shows the power using different priors for regularization. The priors are as follows: π ( m ) = √ N $^{m}$exp ( − √ N ) /m ! for Poisson; π ( m ) = ( N − 1 m − 1 $^{)}$p $^{m}$(1 − p ) ( N − m ) for 

