Stochastic shielding and edge importance for Markov chains with timescale separation
Fig 8
Stochastic shielding and the power spectrum in the 3-state chain for the case where edge importance is reversed (α = 10 shown here).
Panel A shows that the majority of the power comes from the hidden edges (blue) for low frequencies, but the red and blue curves cross at ω ≈ 3, so for high frequencies the majority of the power comes from the observable edges (red). This switch in dominant spectral contributions is reflected in the corresponding Gaussian model trajectories shown in Panel B with the blue trace closely following the black trace, and the red trace deviating from the black trace. This shows that X1,2 best approximates the full process X in this case (whereas X3,4 is the best approximation in the uniform transition rate case shown in Fig 4).