l versus P diagrams showing the posterior samples of a single GP fit with uninformed priors to one example simulation. The horizontal dashed line indicates the simulated spot lifetime, and the vertical dashed line indicates the simulated rotation period. Left: posterior samples fitted to a star with random spot distribution, P_rot = 22 days, and P_life = 110 days. A well-behaved peak is found where both the rotation period and the GP length scale are well constrained. Middle: posterior samples fitted to a star with random spot distribution, P_rot = 22 days, and P_life = 22 days. A posterior plateau with a short length scale spans the entire posterior volume. The posterior of the rotation period is not well constrained due to this plateau; however, some posterior samples form a “triangle” shape at the rotation period. Right: posterior samples fitted to a star with two active longitudes, P_rot = 22 days, and P_life = 11 days. The spots that appear on a similar longitude mimic a coherent signal whose length scale cannot be constrained by the GP, resulting in an “I-shaped” posterior distribution that reaches the upper boundary of the posterior volume.