A view of the EM algorithm that justifies incremental, sparse, and other variants
Learning in graphical models
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Kim and Nelson [1999. State Space Models with Regime Switching. MIT Press, Cambridge, MA] and others extended the framework of state space models involving independent regime changes to the Markov dependent case. The cost of dealing with state space models with Markov switching is high in computational effort because of the number of the possible paths through the chain. Thus it is necessary to make some approximations in order to obtain a computationally feasible algorithm for estimation. The approximations depend on modified smoothing and filtering recursions that can be easily incorporated into an EM algorithm for maximum likelihood estimation. To investigate the accuracy of approximations, we develop a new method to obtain more exact solutions, and then compare the two methods. We apply both methods to a simulated series. The result shows that employing the approximation-based algorithm not only provides accurate results but also leads to a significant reduction in the computational costs. We also apply the methods to an influenza mortality series, in which we develop a model that is general enough to include most structural models useful in monitoring changes of regime. The model proposed has the flexibility to deal with a wide range of problems involving possible regime shifts in pattern that may be seen to occur in many biological, medical and epidemiological studies.