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What is 'hidden' in the HMMs?

Mary K.Kuhner mkkuhner at kingman.gs.washington.edu
Mon Nov 18 16:21:12 EST 2002

In article <arb61p$3l6$1 at mercury.hgmp.mrc.ac.uk>,
Thorsten Burmester  <t_burmester at yahoo.com> wrote:

>Probably a simple question:

>Why are the Hidden Markov Models called "hidden"? What exactly is the
>hidden layer?

The states of the Markov process are not observed directly, but only
indirectly via their effects on some observed variable.

For example, in the HMM used in Phylip for varying mutation rate,
we suppose that there is a Markov process which assigns each site
to a mutation rate class based only on the class of the previous
site.  However, we cannot observe what mutation rate class a base
is in, so this Markov process is "hidden."

Phylip also has a non-hidden mutation rate model in which the
user specifies which sites are in each rate class (this could be
used, for example, for coding sequences where the third position
permits more mutations).

In the non-hidden model it is straightforward to calculate the
likelihood, as we know which class each base is in.  In the
hidden model we must sum over all possible assignments of bases
to classes; luckily there are some computational simplifications
that make this practical.  (The time turns out to be linear
in the number of classes, so an HMM of 8 classes takes only
about 8 times as long as a constant-rates model.)

Mary Kuhner mkkuhner at gs.washington.edu


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