Exploration of how frequency resolution affects the outcome of the beta-HMM.

Panels A and B present analysis from NHP MJ sessions 1–4, panels C and D present analysis from NHP LM sessions 1–5, and panels E and F present analysis from the 9 human EEG sessions. In panels A, C, and E, a portion of the spectrogram is displayed on the top, and two state trajectories are displayed below, estimated from models with H = 51 frequency bands (i.e. the highest possible frequency resolution equal to that of the estimated spectrogram) and H = 7* frequency bands (where 7* frequency bands indicate the canonical frequency bands described in Sec 3.2.2). Panels B, D, and F present the key duration statistics presented in Sec 4.3 and 4.4 across varying frequency-band resolution. With the exception of the models corresponding to 7*, the canonical frequency bands, all other models utilized evenly spaced frequency bands. For each model, 4000 Markov sequences of length N = 2000 were simulated using the estimated transition matrix. The mean duration and interval corresponding to the gamma and slow-delta activities were calculated for each realization of these sequences. Median and 95% confidence bounds across simulated sequences for models with equally spaced frequency bands are indicated in grey and, for the model utilizing canonical frequency bands, in blue. The mean duration and interval calculated from the estimated state trajectory (output of the Viterbi algorithm which uses the maximum likelihood beta-HMM parameters and the observations as input) are indicated by a cross (×) symbol. Note that the 95% confidence intervals of the durations across the varying frequency resolutions almost always overlap. This indicates that the specification of the frequency bands does not have a critical effect on the inferences related to the model dynamics. Thus, in the main manuscript, we chose to present the model estimated from canonical frequency bands that are commonly used to describe neural oscillations. (TIF)