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Bayesian Model Selection for Markov, Hidden Markov,
and Multinomial Models.
Mathias Johansson,
Dirac Research AB
and
Tomas Olofsson
, Signals and Systems, Uppsala University.
IEEE Signal Processing Letters,
Volume 14, No. 2, February 2007, Pages 129-132.
© IEEE
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Abstract:
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Model selection based on observed data sequences is used
to decide between different model structures within the
class of multinomial, Markov, and hidden Markov models.
In a unified Bayesian treatment, we derive posterior
probabilities for different model structures without
assuming prior knowledge of transition probabilities.
We emphasize the following tests:
- Given a particular data sequence of outcomes,
is each state equally likely?
- Do the data support an independent model,
or is a Markov model a more plausible description?
- Are two data sequences generated from
a) the same Markov model?
b) the same hidden Markov model?
For Markov models and independent multinomial models,
all results are exact. For hidden Markov models, the
exact solution is computationally prohibitive,
and instead, an approximate solution is proposed.
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Related publications:
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PhD Thesis
by Mathias Johansson.
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Source:
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