  The increasing availability of data presents an opportunity to calibrate
unknown parameters which appear in complex models of phenomena in the
biomedical, physical and social sciences. However, model complexity often leads
to parameter-to-data maps which are expensive to evaluate and are only
available through noisy approximations. This paper is concerned with the use of
interacting particle systems for the solution of the resulting inverse problems
for parameters. Of particular interest is the case where the available forward
model evaluations are subject to rapid fluctuations, in parameter space,
superimposed on the smoothly varying large scale parametric structure of
interest. {A motivating example from climate science is presented, and ensemble
Kalman methods (which do not use the derivative of the parameter-to-data map)
are shown, empirically, to perform well. Multiscale analysis is then used to
analyze the behaviour of interacting particle system algorithms when rapid
fluctuations, which we refer to as noise, pollute the large scale parametric
dependence of the parameter-to-data map. Ensemble Kalman methods and
Langevin-based methods} (the latter use the derivative of the parameter-to-data
map) are compared in this light. The ensemble Kalman methods are shown to
behave favourably in the presence of noise in the parameter-to-data map,
whereas Langevin methods are adversely affected. On the other hand, Langevin
methods have the correct equilibrium distribution in the setting of noise-free
forward models, whilst ensemble Kalman methods only provide an uncontrolled
approximation, except in the linear case. Therefore a new class of algorithms,
ensemble Gaussian process samplers, which combine the benefits of both ensemble
Kalman and Langevin methods, are introduced and shown to perform favourably.
