Generalised data augmentation and posterior inferences

This paper explores the use of data augmentation in settings beyond the standard Bayesian one. In particular, we show that, after proposing an appropriate generalised data-augmentation principle, it is possible to extend the range of sampling situations in which fiducial methods can be applied by constructing Markov chains whose stationary distributions represent valid posterior inferences on model parameters. Some properties of these chains are presented and a number of open questions are discussed. We also use the approach to draw out connections between classical and Bayesian approaches in some standard settings.