  The answers to data assimilation questions can be expressed as path integrals
over all possible state and parameter histories. We show how these path
integrals can be evaluated numerically using a Markov Chain Monte Carlo method
designed to run in parallel on a Graphics Processing Unit (GPU). We demonstrate
the application of the method to an example with a transmembrane voltage time
series of a simulated neuron as an input, and using a Hodgkin-Huxley neuron
model. By taking advantage of GPU computing, we gain a parallel speedup factor
of up to about 300, compared to an equivalent serial computation on a CPU, with
performance increasing as the length of the observation time used for data
assimilation increases.
