Parameter biases in simulated likelihood analyses for the α model (top) and the r model (bottom). In red and blue, we show the ellipses for the 2D marginalized constraints of the non-stochasticity and the Buzzard stochasticity configurations, respectively. These figures follow Fig. 4 from Krause et al. (2021). For the α model, these are centered on their corresponding 2D marginal MAP. Because of prior volume effects, the marginalized constraints are not centered on the input cosmology. For the r model, there is a systematic bias in the non-stochasticity case that is explained by the sharp upper bound from the prior on r.