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mfouesneau / Nested_Sampling

My playground around nested sampling
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possible error in Model.explore() #2

Closed js850 closed 10 years ago

js850 commented 11 years ago

Hi I was browsing your code when I noticed something which might be an error. It occurs at nest.py line 201 under the comment "Refine step-size to let acceptance ratio converge around 50%"

It's important to refine the step size, but I think it leads to biased sampling if you do it during the Markov Chain. I think about it this way. If the markov chain enters a region where rejection is very likely it will start taking smaller steps. Because of this the markov chain will spend more time in that region. Thus you will sample from this region with a higher probability than you should. it violates detailed balance.

Again, I'm not %100 sure. Normally I do monte carlo sampling with metropolis acceptance criterion (energy and temperature). Adjusting the step size to get a certain acceptance ratio during the MC chain definitely biases those simulations. The simpler acceptance criterion of nested sampling may change the situation.

mfouesneau commented 10 years ago

Sorry I never saw you comment before now.

I think the trick to keep in mind is that nested sampling does not give equal weights to all the points. Instead each point will have an effective weight to use the samples as in MCMC sampling.