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. 2018 Aug 14;12:49. doi: 10.3389/fninf.2018.00049

Figure 10.

Figure 10

The error of the mean, variance and (average) first-order Sobol indices for the quasi-Monte Carlo method (QMC) and polynomial chaos expansions (PC) used on the Hodgkin-Huxley model. The average of the absolute relative error over time of the mean (Equation 3), variance (Equation 4), and first-order Sobol indices (Equation 7) (averaged over all parameters i) of the Hodgkin-Huxley model with three (A) and eleven (B) uncertain parameters. The mean, variance and first-order Sobol indices are calculated using the quasi-Monte Carlo method with 50 re-runs, and polynomial chaos expansion with point collocation. The “exact” solutions are found using the quasi-Monte Carlo method with Ns = 200000 model evaluations to calculate the mean and variance, and Ns = 100000(d + 2) model evaluations (where d is the number of uncertain parameters) to calculate the Sobol indices.