  Most computational approaches to Bayesian experimental design require making
posterior calculations repeatedly for a large number of potential designs
and/or simulated datasets. This can be expensive and prohibit scaling up these
methods to models with many parameters, or designs with many unknowns to
select. We introduce an efficient alternative approach without posterior
calculations, based on optimising the expected trace of the Fisher information,
as discussed by Walker (2016). We illustrate drawbacks of this approach,
including lack of invariance to reparameterisation and encouraging designs in
which one parameter combination is inferred accurately but not any others. We
show these can be avoided by using an adversarial approach: the experimenter
must select their design while a critic attempts to select the least favourable
parameterisation. We present theoretical properties of this approach and show
it can be used with gradient based optimisation methods to find designs
efficiently in practice.
