  A goal of systems biology is to understand the dynamics of intracellular
systems. Stochastic chemical kinetic models are often utilized to accurately
capture the stochastic nature of these systems due to low numbers of molecules.
Collecting system data allows for estimation of stochastic chemical kinetic
rate parameters. We describe a well-known, but typically impractical data
augmentation Markov chain Monte Carlo algorithm for estimating these
parameters. The impracticality is due to the use of rejection sampling for
latent trajectories with fixed initial and final endpoints which can have
diminutive acceptance probability. We show how graphical processing units can
be efficiently utilized for parameter estimation in systems that hitherto were
inestimable. For more complex systems, we show the efficiency gain over
traditional CPU computing is on the order of 200. Finally, we show a Bayesian
analysis of a system based on Michaelis-Menton kinetics.
