Marginal posterior probability on H₀. Grey curves: Individual lens P(H₀|d_i) obtained from Eq. (25) assuming flat priors on the lens model parameters, for ten time-delay lenses. Cyan curve: Statistical combination of the marginal posterior probabilities from the 100 time-delay lenses obtained following Eq. (26). Filled purple histogram: Hierarchical inference from Sect. 5.1 Red histogram: Hierarchical inference with a prior from Paper I, from Sect. 5.2. The vertical dashed line marks the true value of H₀ used to simulate the data.