[Fe(CN) 6 ] 3-/4-process. Traditional heuristic and data analysis optimisation methods produce only single point values for a limited set of parameters and do not quantify the system variability, which is crucial information. Using a statistically based Bayesian inference approach, we are now able to show that the difficulty in achieving reproducibility in the voltammetry is not associated with the impact of random noise, since for each data set we are able to fit the experimental data extremely accurately using a model derived from use of Butler-Volmer electron transfer kinetics, mass transport by planar diffusion, uncompensated resistance and double layer capacitance. Thus, while substantial variation in k 0 from about The left column plots show the samples obtained using the hierarchical model, and these also show the posterior predictive distribution P (•) for each variable, calculated by summing the Gaussian distributions described by the samples of the hyper-parameters µ and Σ (see Figure for histograms of these hyper-parameter samples). For comparison, the right column plots show the samples of θ i with no hierarchical model (and thus no hyper-parameter samples). This is identical to the analysis done in our previous paper. 0.002 to 0.018 cm s -1 is evident in 10 individual experiments at a nominally identical electrode surface (Figure ), conformance to the quasi-reversible model is exceptionally good for each individual experiment.