MCMC with mutually singular distributions (2)

In connection with questions I had posted earlier about the interesting paper of Raphael Gottardo and Adrian Raftery, I got several emails from Raphael that helped with my understanding of the paper, the main point being that having the target being defined against the same measure as the proposal does not prevent from having zero components in this target, thus incorporates within-Gibbs moves quite naturally. Arnaud Doucet also pointed out to me that using kernels with Dirac masses is possible when looking at them from an empirical measure point of view, as explained in this short note. As a coincidence, Raphael also added some comments and explanations on the first post.

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