(A) Statistical relationship of submodes assessed using sampling from generative models. Short trajectory fragments generated using statistics from all 15 submodes individually (gray bars) or submode groups (orange, red bars) were compared to real trajectory fragments ( duration = sec). To generate synthetic sequences, submode transition statistics were either estimated directly from submode sequences in real trajectories (models I,M1,M2), and then used to generate synthetic submode sequences, or transition statistics from state model fits to data were first used to generate state sequences, and then emission statistics fit by each model were used to sample submodes associated with each state, producing submode sequences (HMM,MM). In all cases, submode sequences were compared between real and model-generated sets of sequences. The matched fraction of real sequences, quantifying set overlap, is the average number of exact matches between synthetic and real fragment sets, normalized by the average number of matches between two randomly sampled real sets (Materials and methods sections IV and V, Equation 10). First- and second-order Markov models (M1,M2) perform significantly better than a model that presumes independence between submodes (I) . Five and six state Hidden Markov Models (HMM5,6), as well as 5 and 6 state Markov Models (MM5,6) without hidden states perform well on this generative test . (B) Illustration of the relevant difference between HMM and MM: in a MM (right) observable submodes unambiguously reflect an underlying state (termed a ). In an HMM (left) a given observed submode may arise from more than one underlying state . (C) HMM mean log-likelihood values, plotted against performance on a generative test (fragment set matched fraction, ). Each HMM is represented by a dot and colored by the number of hidden states. (D) Emission probabilities, for a selected 5-state HMM (HMM5, starred in C). Bar colors represent emitting state . Legends list the submodes associated with each state. These are submodes for which is significantly higher than 0. (E) MM performance on likelihood and generative tests as in (C). (F) Emission probabilities, , for the selected MM (MM5, starred in E, and E inset). Modes are colored as in Figure 5.