Violin plots showing the distribution of the derived median rotation periods and length scale hyperparameters of the QP–GP based on 100 simulations per spot lifetime. The blue distribution shows the results obtained from using GP Prior I (wide prior), and the orange distribution shows the results obtained by using GP Prior II (length scale constrained). For the period, the dashed line shows the simulated rotation period and the dash-dotted line the first harmonic at P_rot/2. For the length scale, we show the simulated spot lifetime divided by the determined GP length scale so that the dashed line marks a 1:1 correspondence and the dash-dotted line a factor of 4 between the two. Top: for a random spot distribution on the stellar surface. Bottom: with two active longitudes on the stellar surface.