Unnormalized histogram of Y(δ), the ratio between the probability of cosτ for cosτ ∈ [1 − δ, 1] and cosτ ∈ [ − 1, −1 + δ] for the models of Sects. 3.1–3.3 for δ = 0.01. We also show the result for the LVK default model (Appendix B) for comparison. The solid curves were obtained by sampling the hyperposteriors. The dashed line reports the same quantity, but drawing the model’s hyperparameters from their priors. Values of Y >  1 imply more support for aligned than antialigned spins.