  We present theoretical and practical properties of the affine-invariant
ensemble sampler Markov chain Monte Carlo method. In high dimensions the
affine-invariant ensemble sampler shows unusual and undesirable properties. We
demonstrate this with an $n$-dimensional correlated Gaussian toy problem with a
known mean and covariance structure, and analyse the burn-in period. The
burn-in period seems to be short, however upon closer inspection we discover
the mean and the variance of the target distribution do not match the expected,
known values. This problem becomes greater as $n$ increases. We therefore
conclude that the affine-invariant ensemble sampler should be used with caution
in high dimensional problems. We also present some theoretical results
explaining this behaviour.
