In the results section, the MCMC algorithm described above is used to estimate the parameter values and their posterior distributions from each of the ten repeat runs of the ac voltammetry experiment for the reduction of aqueous 1 mM [Fe(CN) 6 ] 3-, as described in the Experimental methods section. This will allow us to show the degree of variability in the recovered values of the parameters across these ten data sets. This will in turn allow us to postulate that on each repeat of the experiment the parameters θ = {E 0 , k 0 , α, C dl , R u } are themselves drawn from a multivariate normal distribution with mean hyper-parameters µ = ( Ê0 , k0 , α, Ĉdl , Ru ) and a covariance hyper-parameter matrix Σ. Our aim now is to sample from the distributions of µ and Σ to enable us to quantify how θ varies between different experiments.