Efficient Computation of Multiscale Entropy over Short Biomedical Time Series Based on Linear State-Space Models

Figure 2

Estimation of multiscale entropy (MSE) over finite-length realizations of simulated AR processes. Plots depict the exact values (red lines) and the distributions (median and 10th–90th percentiles) of the MSE estimates () computed as a function of the cutoff frequency of the low-pass filter used to eliminate the fast temporal scales of the process for representative parameter settings of Type 1 simulation (a, b) and of Type 2 simulation (c, d). Estimates are obtained using the linear MSE (LMSE) method proposed in this study (a, c) and using the refined MSE (RMSE) method proposed in [11] (b, d). In simulated AR processes, RMSE estimates exhibit high bias and a variance increasing with the time scale, while LMSE estimates display high computational reliability at all time scales.

(a) LMSE

(b) RMSE

(c) LMSE

(d) RMSE