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Subsections
A Poisson mixture models is defined by the two (1-D) arrays:
- wght
- Mixture weights (positive and sum to 1)
- rate
- Corresponding rates (parameters of the Poisson distributions)
A Poisson HMM is defined by
- TRANS
- The transition matrix of the hidden chain
- rate
- Corresponding rates (parameters of the Poisson distributions)
A negative binomial HMM is defined by
- TRANS
- The transition matrix of the hidden chain
- alpha
- Corresponding (positive) shape parameters
- beta
- Corresponding (positive) inverse scales
where the Negative Binomial distribution is such that
which has mean
and variance
. The
negative binomial distribution can be viewed as a Poisson (continuous) mixture
for which the rate follows a
distribution
(this is the method used for simulating from the model in nbh_gen
). If
you don't know what the negative binomial distribution is, you should refer,
for instance, to [8] or perhaps to [9].
Contrary to what was the case for the H2M main functions, the H2M/cnt HMM
functions are mostly intended to deal with ergodic models which are estimated
from a single long observation sequence (whereas left-right HMMs such as those
used in speech processing need to be trained using multiple observation
sequences). With a single (long) training sequence, the initial distribution is
a parameter that has little influence and that cannot be estimated
consistently. Taking this into account, it is assumed that the initial
distribution (usually called pi0
in the H2M functions is uniform
(equal probabilities for all states of the model).
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Olivier Cappé, Aug 24 2001