  Data assimilation (DA) solves the inverse problem of inferring initial
conditions given data and a model. Here we use biophysically motivated
Hodgkin-Huxley (HH) models of avian HVCI neurons, experimentally obtained
recordings of these neurons, and our data assimilation algorithm to infer the
full set of parameters and a minimal set of ionic currents precisely
reproducing the observed waveform information. We find many distinct validated
sets of parameters selected by our DA method and choice of model. We conclude
exploring variations on the inverse problem applied to neurons producing
accurate or inaccurate results; by manipulating data presented to the
algorithm, varying sample rate and waveform; and by manipulating the model by
adding and subtracting ionic currents.
