Googling for information on approximate Bayesian computation algorithms, I found this seminar given by Richard Wilkinson. I really like that this site has both video of Richard and as well as the slides which automatically transition while you are watching the presentation. I'm sure somebody had to put the timings in behind the scenes and I appreciate that. I'm still confused as to why I don't see an ABC-Gibbs sampler method in my searching of ABC methods. In particular, I mean a method where
1. $\theta\sim p(\theta|D')$
2. $D'\sim p(\cdot|\theta)$ where $latex D'$ is accepted if it is reasonably close to the true data $latex D$ in the ABC fashion
This seems like a straight-forward "ABC" algorithm that does not appear to be covered in what I have read of the ABC literature. Probably this is a deficiency of my reading rather than a deficiency of the literature. I'm guessing that it is a special case (somehow) of one of the algorithms that have already been outlined. Anybody help me out? P.S. Yes, I really need to get a LaTeX plugin. [I beat my own post to press and installed the plug-in.]