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Oh, I'd actually found this approach searching a while back.

It frames all Markov Chain Monte Carlo as a variation of slice sample. I like it because it makes the process fairly simple but I have tried to implement it yet.

https://en.wikipedia.org/wiki/Slice_sampling




Another way to look at this: slice sampling is analogous to taking the Lebesgue integral rather than the Riemann integral (we sum small horizontal strips rather than vertical bars).




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