Figure 1

Accuracy of p -values in simulations. (A) A typical simulation matching the OpWise model. The solid line shows the estimated log odds for each gene ($\log \frac{P\left({\mu }_i>0\right)}{1-P\left({\mu }_i>0\right)}$) as a function of the "ideal" log odds based on the true values of the hyperparameters. The slope is from linear regression with the intercept fixed at zero. (B) Slopes from 50 simulations for each data set's hyperparameters. The boxes show the first and third quartiles and the medians, the whiskers show the most extreme point within 1.5 times the inter-quartile range of the box, and the points indicate outliers. (C) A typical "uncoupled" simulation where means and variances were independent. We sorted the genes by their estimated log odds into 10 bins of equal size. For each bin, a point shows the true log odds (from the number of genes with μ _i > 0 and μ _i < 0) and the average of the estimated log odds. Logistic regression gave a slope of 0.97 (solid line). (D) Slopes from 50 uncoupled simulations for each data set and from 50 heavy-tailed simulations for the ecox data set. The dashed lines in (A) and (C) show x = y.