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Hi! Once upon a time we were talking about something like this... I only vaguely remember it, so interpret this generously, through a fuzzy lens:
There's some known way of trying to sample a random distribution which is a bit like Markov chain Monte Carlo, but instead of a single point (or "particle") walking around randomly, you have a bunch of particles, which can split at various times, and/or die out. Or something like that. Do you remember what I'm talking about? What was it?
All of a sudden this seems exactly like the "phylogenetic trees" discussed on the blog. In these trees we have a Markov chain of random DNA evolution along each edge, but sometimes species split (or die out, but people don't talk about that as much).
I may be modifying my memory of our old conversation to make it seem more similar to the new stuff.