Figure shows an example of the initial fitting process for experimental data set 1. Once the best fit for each data set was obtained using maximum likelihood estimation and the cma-es optimisation algorithm, each of the bottom level MCMC algorithms was initialised at these points. Then Algorithm 1 was used to generate 5,000 samples (10,000 total samples, of which the first 5,000 was discarded as burn-in) of the parameters θ i and hyper-parameters µ and Σ. ). Simulation parameters were obtained by maximum likelihood estimate, and their values in dimensional units were E 0 = 0.214 V, k 0 = 0.010 cm s -1 , α = 0.528, C dl = 16.9 µF cm -2 , R u = 0.00 Ω.