Figure 4.

Convergence of ABC posterior to the true posterior as ε → 0 for the mono-molecular chain inference problem. Marginal posteriors are plotted for ε = 50 (blue solid), ε = 25 (red solid), ε = 12.5 (yellow solid) and ε = 0 (black dotted). Here, the ε = 0 case corresponds to the exact likelihood using the chemical master equation solution. (a) Marginal posteriors for k₁, (b) marginal posteriors for k₂ and (c) marginal posteriors for k₃. The true parameter values (black dashed) are k₁ = 1.0, k₂ = 0.1 and k₃ = 0.05. Note that the exact Bayesian posterior does not recover the true parameter for k₃. The priors used are $k_1\sim \mathcal{U}(0,3)$, $k_2\sim \mathcal{U}(0,0.3)$ and $k_3\sim \mathcal{U}(0,0.15)$. (Online version in colour.)