  We describe the R package acebayes and demonstrate its use to find Bayesian
optimal experimental designs. A decision-theoretic approach is adopted, with
the optimal design maximising an expected utility. Finding Bayesian optimal
designs for realistic problems is challenging, as the expected utility is
typically intractable and the design space may be high-dimensional. The package
implements the approximate coordinate exchange algorithm to optimise (an
approximation to) the expected utility via a sequence of conditional
one-dimensional optimisation steps. At each step, a Gaussian process regression
model is used to approximate, and subsequently optimise, the expected utility
as the function of a single design coordinate (the value taken by one
controllable variable for one run of the experiment). In addition to functions
for bespoke design problems with user-defined utility functions, acebayes
provides functions tailored to finding designs for common generalised linear
and nonlinear models. The package provides a step-change in the complexity of
problems that can be addressed, enabling designs to be found for much larger
numbers of variables and runs than previously possible. We provide tutorials on
the application of the methodology for four illustrative examples of varying
complexity where designs are found for the goals of parameter estimation, model
selection and prediction. These examples demonstrate previously unseen
functionality of acebayes.
