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Implement Poisson output model (for FRET) #3

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franknoe opened this issue Feb 27, 2015 · 0 comments
Open

Implement Poisson output model (for FRET) #3

franknoe opened this issue Feb 27, 2015 · 0 comments

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@franknoe
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Poisson processes can be used to model time-binned single-molecule FRET data. This model is also useful for the output model including background noise contributions used in Keller et al, JACS 2014 (Just Poisson processes where the emission rates are reduced by the background emission rates).

For this kind of output model it might be necessary to use log-probabilities, because output probabilities for observations with many photons can run into underflow problems. This might, however, not be a problem if we compute output probabilities over all states for one observation symbol at once (starting in the log space and shifting by an appropriate constant before moving into lin space). This way some output probabilities will likely be zero, but we still get nonzero output probabilities in the states with significant probability. I believe this is enough to avoid problems with the forward-backward, Viterbi and path sampling algorithms.
However we should then not give access to a routine that calculates single output probabilities of a symbol o_t given a particular state i (function p_o_i), because we need to compute the output probabilities for all symbols in order to determine the appropriate shifting constant that avoids underflow.

@franknoe franknoe self-assigned this Feb 27, 2015
@franknoe franknoe removed their assignment Mar 28, 2015
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