  We consider Bayesian analysis on high-dimensional spheres with angular
central Gaussian priors. These priors model antipodally symmetric directional
data, are easily defined in Hilbert spaces and occur, for instance, in Bayesian
binary classification and level set inversion. In this paper we derive
efficient Markov chain Monte Carlo methods for approximate sampling of
posteriors with respect to these priors. Our approaches rely on lifting the
sampling problem to the ambient Hilbert space and exploit existing
dimension-independent samplers in linear spaces. By a push-forward Markov
kernel construction we then obtain Markov chains on the sphere, which inherit
reversibility and spectral gap properties from samplers in linear spaces.
Moreover, our proposed algorithms show dimension-independent efficiency in
numerical experiments.
