TY - JOUR
T1 - Extraction of parameters and their error distributions from cyclic voltammograms using bootstrap resampling enhanced by solution maps
T2 - Computational study
AU - Bieniasz, Lesław K.
AU - Rabitz, Herschel Albert
PY - 2006/12/15
Y1 - 2006/12/15
N2 - The conventional determination of model parameter errors in least-squares regression of experimental cyclic voltammetric data assumes validity of local approximations (e.g., linearization) in the parameter space and normal distributions of the data and parameter errors. Such assumptions may not always be satisfied in practice. Bootstrap resampling techniques present a more universally applicable approach to error estimation, which until now has not been used in cyclic voltammetric studies, owing to the high costs of the required voltammogram simulations. We demonstrate that the burden of computing voltammograms can be significantly reduced by the use of high-dimensional model representation (HDMR) solution mapping techniques, thereby making it feasible to apply the bootstrap data analysis in cyclic voltammetry. We perform computational experiments with bootstrap resampling, enhanced by HDMR maps, for a typical cyclic voltammetric model (i.e., the Eqrev Cirr Eqrev reaction mechanism at a planar macroelectrode under semi-infinite, pure diffusion transport conditions). The experiments reveal that the bootstrap distributions of the estimated parameters provide a satisfactory quantification of the parameter errors and can also be used for detecting statistical correlations of the parameters.
AB - The conventional determination of model parameter errors in least-squares regression of experimental cyclic voltammetric data assumes validity of local approximations (e.g., linearization) in the parameter space and normal distributions of the data and parameter errors. Such assumptions may not always be satisfied in practice. Bootstrap resampling techniques present a more universally applicable approach to error estimation, which until now has not been used in cyclic voltammetric studies, owing to the high costs of the required voltammogram simulations. We demonstrate that the burden of computing voltammograms can be significantly reduced by the use of high-dimensional model representation (HDMR) solution mapping techniques, thereby making it feasible to apply the bootstrap data analysis in cyclic voltammetry. We perform computational experiments with bootstrap resampling, enhanced by HDMR maps, for a typical cyclic voltammetric model (i.e., the Eqrev Cirr Eqrev reaction mechanism at a planar macroelectrode under semi-infinite, pure diffusion transport conditions). The experiments reveal that the bootstrap distributions of the estimated parameters provide a satisfactory quantification of the parameter errors and can also be used for detecting statistical correlations of the parameters.
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U2 - 10.1021/ac061167z
DO - 10.1021/ac061167z
M3 - Article
C2 - 17165836
AN - SCOPUS:33845519908
SN - 0003-2700
VL - 78
SP - 8430
EP - 8437
JO - Analytical Chemistry
JF - Analytical Chemistry
IS - 24
ER -