Fig. 2

Illustration of the linear co-data model. Given the true effect sizes \(\beta _k^2\) (points), the prior parameters may be interpreted as follows: (i) the scaling factor \(\tau ^2_{global}\) (grey dashed line) quantifies the overall expected effect size, which is independent of the co-data; (ii) each scaled co-data variable weight \(\tau ^2_{global}\gamma ^{(d)}_g\) (black dashed lines) quantifies the expected effect size in a group for categorical co-data or the expected increase in effect size for one unit increase in continuous co-data, i.e. the slope of the line; (iii) the co-data weights \(w_d\), \(d=1,2\), then quantify importance of multiple co-data sets. Note that in practice, the true effect sizes are unknown and estimation of the prior parameters is done by the empirical Bayes approach described below