  We present a new method for inferring hidden Markov models from noisy time
sequences without the necessity of assuming a model architecture, thus allowing
for the detection of degenerate states. This is based on the statistical
prediction techniques developed by Crutchfield et al., and generates so called
causal state models, equivalent to hidden Markov models. This method is
applicable to any continuous data which clusters around discrete values and
exhibits multiple transitions between these values such as tethered particle
motion data or Fluorescence Resonance Energy Transfer (FRET) spectra. The
algorithms developed have been shown to perform well on simulated data,
demonstrating the ability to recover the model used to generate the data under
high noise, sparse data conditions and the ability to infer the existence of
degenerate states. They have also been applied to new experimental FRET data of
Holliday Junction dynamics, extracting the expected two state model and
providing values for the transition rates in good agreement with previous
results and with results obtained using existing maximum likelihood based
methods.
