Behavior of the beta prior for systematic offsets in an echelle diagram. The squares represent model frequencies, while the shaded "trails" indicate the prior probability density for varying Δ _i . The left panel uses equal Δ _max, whereas the right panel uses a power-law Δ _max with exponent b = 4.9 (see Section 4.1). Note that the uniform prior is not shown, since it simply assigns a constant probability density.