Integrated Continuous-time Hidden Markov Models
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Motivated by applications in movement ecology, in this paper I propose a new class of integrated continuous-time hidden Markov models in which each observation depends on the underlying state of the process over the whole interval since the previous observation, not only on its current state. I show that under appropriate conditioning, such a model can be regarded as a conventional hidden Markov model, enabling efficient evaluation of its likelihood without sampling of its state sequence. This leads to an algorithm for inference which is more efficient, and scales better with the number of data, than existing methods. An application to animal movement data is given.
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