  Recently, we have introduced the use of techniques drawn from Bayesian
statistics to recover kinetic and thermodynamic parameters from voltammetric
data, and were able to show that the technique of large amplitude ac
voltammetry yielded significantly more accurate parameter values than the
equivalent dc approach. In this paper we build on this work to show that this
approach allows us, for the first time, to separate the effects of random
experimental noise and inherent system variability in voltammetric experiments.
We analyse ten repeated experimental data sets for the $[$Fe(CN)$_6]^{3-/ 4-}$
process, again using large-amplitude ac cyclic voltammetry. In each of the ten
cases we are able to obtain an extremely good fit to the experimental data and
obtain very narrow distributions of the recovered parameters governing both the
faradaic (the reversible formal faradaic potential, $E_0$, the standard
heterogeneous charge transfer rate constant $k_0$, and the charge transfer
coefficient $\alpha$) and non-faradaic terms (uncompensated resistance, $R_u$,
and double layer capacitance, $C_{dl}$). We then employ hierarchical Bayesian
methods to recover the underlying "hyperdistribution" of the faradaic and
non-faradaic parameters, showing that in general the variation between the
experimental data sets is significantly greater than suggested by individual
experiments, except for $\alpha$ where the inter-experiment variation was
relatively minor. Correlations between pairs of parameters are provided, and
for example, reveal a weak link between $k_0$ and $C_{dl}$ (surface activity of
a glassy carbon electrode surface). Finally, we discuss the implications of our
findings for voltammetric experiments more generally.
