Dear Pedro,

The answer to your question may be found in the below link.

http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/Randomise/Theory

Dear Pedro,

The answer to your question may be found in the below link.

http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/Randomise/Theory

It is usually 1000.

The higher the number, the closer the p-value will be to the p-value that would be found by systematically examining all possible permutations. See http://dx.doi.org/10.1556/ComEc.14.2013.2.5

Best resource to read about it would probably be Manly 1997 "Randomization, Bootstraps and Monte Carlo Methods"...

From my little experience with Monte-Carlo simulations, you can try different numbers of permutations (100, 1000, 2000, 5000,...) and then graph your resulting statistics. You can then see when increasing the number of permutations stops significantly increasing the accuracy of your test: you will reach a plateau.

Dear Pedro,

As Sergio said, it depends on your problem and your model. Let's say you want to find error probability and you expect to have values between 10^-1 and 10^-4. In this case, you should have at least 10^5 permutations, which is obtained by:

10 / (\min(10^-1 and 10^-4))).

But in general as Valério said, the higher this number, the better and more precise results you will obtain.

As the answer is indeed model dependent you need to make a figure-of-merit in order to stablish the optimal value. Hopefully you will reach a plateau.