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Binomial, with p = 0 . 119 so that the penalty becomes that of the Akaike information criterion (i.e., log π ( I| m ) π ( m ) = − 2 m ); π ( m ) = 1 /K for fixed K for Uniform. We also considered the prior in Jiang et al. (2014), resulting in the DS test with penalty − λ$_{0}$ log N ( m − 1). According to the recommendation in Jiang et al. (2014), we chose the value of λ$_{0}$ so that the level under the null is as close as possible to 0.05 from below, so λ$_{0}$ = 1 . 11088 for N = 100, and λ$_{0}$ = 0 . 904 for N = 500. The Poisson prior (with rate √ N ) was by far the best among all priors considered, and its power was comparable to that of the minimum p -value displayed in Table 6. 

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For sample size N = 100, we examined the distributions depicted in Figure 10, and we used 20000 simulated data sets, in each of the configurations. Table 9 and Figure 11 show the power for the setups in Figure 10. These results concur with the results in Section 4.1 for N = 500, and show that if the number of intersections of the two distributions is at least four, tests statistics with m ≥ 4 have an advantage. 

