On residual and guided proposals for diffusion bridge simulation

Abstract: Recently Whitaker et al. (2017) considered Bayesian estimation of diffusion driven mixed effects models using data-augmentation. The missing data, diffusion bridges connecting discrete time observations, are drawn using a "residual bridge construct". In this paper we compare this construct (which we call residual proposal) with the guided proposals introduced in Schauer et al. 2017. It is shown that both approaches are related, but use a different approximation to the intractable stochastic differential equation of the true diffusion bridge. It reveals that the computational complexity of both approaches is similar. Some examples are included to compare the ability of both proposals to capture local nonlinearities in the dynamics of the true bridge.