  In this paper we describe a general probabilistic framework for modeling
waveforms such as heartbeats from ECG data. The model is based on segmental
hidden Markov models (as used in speech recognition) with the addition of
random effects to the generative model. The random effects component of the
model handles shape variability across different waveforms within a general
class of waveforms of similar shape. We show that this probabilistic model
provides a unified framework for learning these models from sets of waveform
data as well as parsing, classification, and prediction of new waveforms. We
derive a computationally efficient EM algorithm to fit the model on multiple
waveforms, and introduce a scoring method that evaluates a test waveform based
on its shape. Results on two real-world data sets demonstrate that the random
effects methodology leads to improved accuracy (compared to alternative
approaches) on classification and segmentation of real-world waveforms.
