Fig. 1.

An overview of the ABC partial rejection control technique fitting to one parameter and for three steps. The true underlying likelihood is shown at the bottom, with 25, 50 and 75 percentiles shown as red dotted lines. A number of particles (N) are fixed at the beginning, here $N=8$. In the first step, these particles are drawn from a prior distribution, which is uniform between two values (top row, corresponds to steps 1–2 in Algorithm 1). For a given tolerance, a new particle is drawn for the updated tolerance ${ϵ}_1$ by choosing a particle at random, perturbing it slightly and then running a model evaluation (step 5–6 in Algorithm 1). It then checks if the tolerance of that particle is below ${ϵ}_1$, the particle is then either accepted (blue) or rejected (shown in red) (steps 7–8 in Algorithm 1). This procedure continues until all N particles are accepted at the new tolerance level (steps 9–10). As the tolerance decreases, the particles converge onto the target distribution (shown in the bottom row). (For interpretation of the references to color in text/this figure legend, the reader is referred to the web version of the article.)