State-space models (SSM) with Markov switching offer a powerful framework for detecting multiple regimes in time series, analyzing mutual dependence and dynamics within regimes, and assessing transitions between regimes. These models however present considerable computational challenges due to the exponential number of possible regime sequences to account for. In addition, high dimensionality of time series can hinder likelihood-based inference. To address these challenges, novel statistical methods for Markov-switching SSMs are proposed using maximum likelihood estimation, Expectation-Maximization (EM), and parametric bootstrap. Solutions are developed for initializing the EM algorithm, accelerating convergence, and conducting inference. These methods, which are ideally suited to massive spatio-temporal data such as brain signals, are evaluated in simulations and applications to EEG studies of epilepsy and of motor imagery are presented.
ASJC Scopus subject areas
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics
- Statistics and Probability