  We propose simple methods for multivariate diffusion bridge simulation, which
plays a fundamental role in simulation-based likelihood and Bayesian inference
for stochastic differential equations. By a novel application of classical
coupling methods, the new approach generalizes a previously proposed simulation
method for one-dimensional bridges to the multi-variate setting. First a method
of simulating approximate, but often very accurate, diffusion bridges is
proposed. These approximate bridges are used as proposal for easily
implementable MCMC algorithms that produce exact diffusion bridges. The new
method is much more generally applicable than previous methods. Another
advantage is that the new method works well for diffusion bridges in long
intervals because the computational complexity of the method is linear in the
length of the interval. In a simulation study the new method performs well, and
its usefulness is illustrated by an application to Bayesian estimation for the
multivariate hyperbolic diffusion model.
