To test our inference procedure and algorithms we make use of "synthetic" test data i.e. we generate ten synthetic data sets by solving Equations 2 to 8 for a randomly chosen set of values of θ = (E 0 , k 0 , α, C dl , R u ), drawn from a multivariate normal distribution with mean θ true = (7.27, 2.01, 0.53, 3.70 × 10 -3 , 1.06 × 10 -2 ) (in non-dimensional units), and standard deviation σ true = (0.06, 0.7, 0.005, 0.7 × 10 -3 , 0.3 × 10 -2 ). We then add randomly generated Gaussian noise at each time point with zero mean and standard deviation of 0.3% of the maximum current (chosen to match the experimental noise level).