Yeah, that's what I meant, the one particle bit.

Frequently you'll see things along the lines of "we ran 10,000 MCMC iterations to find the solution" and my first thought is "that must be a lot of wasted cycles."

I think I see what you mean now about the parallelization by decomposing the variables (splitting the problem into i separate problems which can be chained independently?)-- I didn't know that was a possibility. I'll have to look at that.