## MR-HMM Likelihood function

The MR-HMM likelihood function is a complete statistical model of the concatenated input time-series data . By expanding, we can write

 (14.1)

where is the set of all possible segmentations, and is the a priori probability of that segmentation, and are the MR-HMM parameters. A segmentation defines not only the segment sizes , but also the sub-class 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 time-series data in the segment.

Baggenstoss 2017-05-19