  Generalised Bayesian inference updates prior beliefs using a loss function,
rather than a likelihood, and can therefore be used to confer robustness
against possible mis-specification of the likelihood. Here we consider
generalised Bayesian inference with a Stein discrepancy as a loss function,
motivated by applications in which the likelihood contains an intractable
normalisation constant. In this context, the Stein discrepancy circumvents
evaluation of the normalisation constant and produces generalised posteriors
that are either closed form or accessible using standard Markov chain Monte
Carlo. On a theoretical level, we show consistency, asymptotic normality, and
bias-robustness of the generalised posterior, highlighting how these properties
are impacted by the choice of Stein discrepancy. Then, we provide numerical
experiments on a range of intractable distributions, including applications to
kernel-based exponential family models and non-Gaussian graphical models.
