FIG. 2: Averaged simulated log-likelihood landscapes for (a, b) = (20, 2.5) and γ = 100. Landscapes for single time-courses (left) are shown with contour lines drawn at intervals of 1 unit; contours for landscapes obtained from 20 time-courses (right) are drawn at intervals of 10 units. The averaged log-likelihood landscapes generated using a single time-course for the zeroth-order propagator, Eq. (2), (A), the uniform propagator, Eq. (3), (B), and a finite state projection approximation (C) for a single time-course each display a bias of the MLE with respect to the true model parameters (a∗, b∗). Notably, the landscape of the uniform propagator (B) shows distortions arising from non-physical transition probabilities for some parameter pairs (a, b). As the number of trajectories is increased to 20, the MLE converges to (a∗, b∗) for each of the zeroth-order propagator (D), uniform propagator (E), and the finite state projection (F). The averaged log-likelihood resulting from the finite state projection seems to be most tightly-peaked around the true parameter values (a∗, b∗).
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