The MRHMM likelihood function is a complete
statistical model of the concatenated input timeseries data .
By expanding, we can write
where is the set of all possible segmentations,
and
is the a priori probability of that segmentation,
and
are the MRHMM parameters.
A segmentation defines not only the
segment sizes , but also the subclass identities ,
as ranges over all the segments in .
Due to the conditional independence of the segments, we may write

(14.2) 
where is a segment within segmentation ,
is the subclass identity, and is the
timeseries data in the segment.
Baggenstoss
20170519