  We introduce a new residual-bridge proposal for approximately simulating
conditioned diffusions. This proposal is formed by applying the modified
diffusion bridge approximation of Durham and Gallant (2002) to the difference
between the true diffusion and a second, approximate diffusion driven by the
same Brownian motion, and can be viewed as a natural extension to recent work
on residual-bridge constructs (Whitaker et al., 2016). This new proposal
attempts to account for volatilities which are not constant and can therefore
lead to gains in efficiency over the recently proposed residual-bridge
constructs in situations where the volatility varies considerably, as is often
the case for larger inter-observation times and for time-inhomogeneous
volatilities. These potential gains in efficiencies are illustrated via a
simulation study.
