A Comparison of Bayesian Inference Strategies for Parameterisation of Large Amplitude AC Voltammetry Derived from Total Current and Fourier Transformed Versions

Use of carefully designed computer supported parameterisation methods in voltammetric studies can provide highly robust and accurate methods for simultaneously quantifying the large number of parameters present in complex electrochemical reactions. In this study, a computer program has been developed to parameterise large amplitude AC voltammetric data using mathematical optimisation in combination with Bayesian inference algorithms for calculating posterior distributions of parameters and hence uncertainties in parameter values. The computer program has been applied to objective functions, relevant to total AC current, frequency domain data in the form of the power spectrum derived from Fourier transformation and multivariate based methods using the resolved harmonic data. The robustness of the objective functions have been confirmed and Bayesian inference methods have been validated using “noisy” synthetic and experimental data for the [Fe(CN)₆]^3−/4− reduction process in aqueous 3.0 M KCl electrolyte at a gold electrode. It was found that the harmonic based Bayesian inference methods outperformed other methods in parameterisation of the thermodynamics and electrode kinetics of the close to reversible [Fe(CN)₆]^3−/4− process due to their ability to compensate for non-ideality in the modelling and the superior parameter sensitivities available in the higher harmonics. The computer supported and heuristic methods were compared. Their advantages and limitations are discussed.