  Stochastic process models are now commonly used to analyse complex
biological, ecological and industrial systems. Increasingly there is a need to
deliver accurate estimates of model parameters and assess model fit by
optimizing the timing of measurement of these processes. Standard methods to
construct Bayes optimal designs, such as the well known \Muller algorithm, are
computationally intensive even for relatively simple models. A key issue is
that, in determining the merit of a design, the utility function typically
requires summaries of many parameter posterior distributions, each determined
via a computer-intensive scheme such as MCMC. This paper describes a fast and
computationally efficient scheme to determine optimal designs for stochastic
process models. The algorithm compares favourably with other methods for
determining optimal designs and can require up to an order of magnitude fewer
utility function evaluations for the same accuracy in the optimal design
solution. It benefits from being embarrassingly parallel and is ideal for
running on multi-core computers. The method is illustrated by determining
different sized optimal designs for three problems of increasing complexity.
