2 ms·
Btw, I looked at https://arxiv.org/pdf/1509.03808.pdf https://arxiv.org/pdf/1509.03808.pdf and I don’t understand this paragraph at the end of the first page:
by kgwgk 6y ago
Btw, I looked at https://arxiv.org/pdf/1509.03808.pdf https://arxiv.org/pdf/1509.03808.pdf and I don’t understand this paragraph at the end of the first page:
“To simulate the system, waiting times w_kj are generated for all candidate states k, and the shortest waiting time i = argmin_k w_kj is chosen. We call this shortest waiting time the holding time. A transition is then performed to state i after a delay of length w_ij.”
Say there are three states A, B, C and the transition rate to C from A or B is low. Wouldn’t your “simulation” jump endlessly between A and B without ever (or never again) visiting C?
I may be missing something.
- andbberger 6y agoOh god don't read that... The transition rates for each individual state transition are drawn from an exponential distribution with a rate dependent on the energy difference between the states. So, no, C will be visited with some probability. There are many problems with that paper, but validity of the sampling algorithm is not one of them. It is an unbiased sampler and will eventually converge to the sampled distribution (as proved in the paper). How long that convergence will take is another store. It remains unclear whether this approach converges faster than your garden-variety Markov chain and if so when and why.
- kgwgk 6y agoThanks for your answer. Sorry, I don’t why i did interpret “waiting times” as “expected waiting times” when it was right in the preceding paragraph how they were sampled.
- andbberger 6y agoNothing to apologize for