Fig. 7
Study of the invertibility of the tMGE representation. (A) shows the dependence of the coefficients of \(K_{I}^{0}\), \(K_{A}^{0} ,\) and \(K_{\varepsilon }\) in Eq. (36) on mixing time for different exchange rates. The lack of dependence on mixing time of the coefficients of \(K_{I}^{0}\) and \(K_{A}^{0} ,\) at zero exchange rate means that these parameters cannot be disentangled from their long-time variants \(K_{I}^{\infty }\) and \(K_{A}^{\infty }\). At intermediate exchange rates, all parameters of Eq. (36) can be estimated from the signals. At very fast exchange (k = 200 s−1), the dependence on mixing time is again lost, making it difficult to disentangle the exchange rate from transient kurtosis. Panel B shows bias and precision (1 std. dev.) in parameter estimates obtained by generating signals using the tMGE representation (Eq. 36), corrupting the signals with Rice-distributed noise at SNR = 200 and fitting the same equation to those signals. The figure shows high bias and low precision at very slow and fast exchange rates, indicating inability to invert the tMGE representation in these extremes. The representation is, however, invertible at intermediate exchange rates.
