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jBillou added subsection_hidden_Markov_models_for__.tex
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\subsection{hidden Markov models for phase inference}
In this work we developed a novel method (TODO:true?) of inferring phases from data using hidden Markov models. We found that this method is adequate to decode real-world data, as it allows to specify a noise model as well as the underlying stochastic dynamics, and to explicitly take into account features of the data like amplitude, making the hypothesis underlying the analysis more manifest. A consequence of this is that several parameters have to be calibrated. Note however that because we learn the waveform, linking the phase to the data, from a large collection of time traces, our inferred phase is invariant under transformations of the data, unlike methods based on the Hilbert transform \cite{Kralemann_2008}.
