Fig. 3: Segmentation of filtered displacement time series.

a Displacement time series of a 2-state Brownian particle, with \({\bar{\tau }}_{1}={\bar{\tau }}_{2}=20\), and D₂/D₁ = 5. b Displacement distribution of the N_t unfiltered trajectories fitted to a Rayleigh mixture according to Eq. (6). The overlap between the displacement distributions of individual states is shaded. c Displacement distribution of the same N_t trajectories, but now after filtering using the optimal filter width f* fitted to a sum of two Gaussians, according to Eq. (8). d Inferred time series of the probability p_i of belonging to the diffusive state i, extracted from the filtered displacement distribution. The black dashed line indicates the threshold, corresponding to p_i = 0.5. e The displacement time series in (a) after filtering using the optimal filter width f*. The dashed line corresponds to the optimised threshold between states 1 and 2, inferred by the intersection point between the two fitted Gaussians in (c). f Comparison between the ground truth and inferred state timeseries of the trajectory (top panel) and the inferred probability of misclassification, \({p}_{{\rm{mc}}}\equiv \min ({p}_{1},{p}_{2})\) (bottom panel, c.f. Fig. 3d).