  Recent studies have proposed that one can summarize brain activity into
dynamics among a relatively small number of hidden states and that such an
approach is a promising tool for revealing brain function. Hidden Markov models
(HMMs) are a prevalent approach to inferring such neural dynamics among
discrete brain states. However, the impact of assuming Markovian structure in
neural time series data has not been sufficiently examined. Here, to address
this situation and examine the performance of the HMM, we compare the model
with the Gaussian mixture model (GMM), which is with no temporal regularization
and thus a statistically simpler model than the HMM, by applying both models to
synthetic time series generated from empirical resting-state functional
magnetic resonance imaging (fMRI) data. We compared the GMM and HMM for various
sampling frequencies, lengths of recording per participant, numbers of
participants, and numbers of independent component signals. We find that the
HMM attains a better accuracy of estimating the hidden state than the GMM in a
majority of cases. However, we also find that the accuracy of the GMM is
comparable to that of the HMM under the condition that the sampling frequency
is reasonably low (e.g., TR = 2.88 or 3.60 s) or the data is relatively short.
These results suggest that the GMM can be a viable alternative to the HMM for
investigating hidden-state dynamics under this condition.
