Has anyone come across this? I 'invented' it last night, but I'm sure it was discovered decades ago- either that, or it's wrong.(adsbygoogle = window.adsbygoogle || []).push({});

The standard problem is to sample according to a probability distribution P(x).

In standard MMC, this is achieved by:

1) Pick a trial point x' at random within x-dx..x+dx.

2) If P(x')>P(x) then accept the move- set x=x' and return to 1

3) If P(x')<P(x) then accept the move with a probability P(x')/P(x). If move is accepted then set x=x' and return to 1. If move is rejected- just return to 1 without changing x.

-------------------------------

My variation is this

1) Pick a trial point x' at random within x-dx..x+dx

2) Accept move with probability P(x')/(P(x)+P(x')). If move is accepted then set x=x' and return to 1. If move is rejected- just return to 1 without changing x.

It's quite easy to show that both methods obey 'detailed balance'. I'm not sure if there's any advantage of the variation- but it's interesting that an alternative to the standard algorithm exists.

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# An alternative to Metropolis Monte Carlo

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