Electroencephalographam (EEG) monitoring of neural activity is widely used for identifying underlying brain states. For inference of brain states, researchers have often used Hidden Markov Models (HMM) with a fixed number of hidden states and an observation model linking the temporal dynamics embedded in EEG to the hidden states. The use of fixed states may be limiting, in that 1) pre-defined states might not capture the heterogeneous neural dynamics across individuals and 2) the oscillatory dynamics of the neural activity are not directly modeled. To this end, we use a Hierarchical Dirichlet Process Hidden Markov Model (HDP-HMM), which discovers the set of hidden states that best describes the EEG data, without a-priori specification of state number. In addition, we introduce an observation model based on classical asymptotic results of frequency domain properties of stationary time series, along with the description of the conditional distributions for Gibbs sampler inference. We then combine this with multitaper spectral estimation to reduce the variance of the spectral estimates. By applying our method to simulated data inspired by sleep EEG, we arrive at two main results: 1) the algorithm faithfully recovers the spectral characteristics of the true states, as well as the right number of states and 2) the incorporation of the multitaper framework produces a more stable estimate than traditional periodogram spectral estimates.
