Tim Peters <t...@python.org> added the comment:

Thanks for the NumPy discussion link, Mark!  Did that set a world record for an 
issue report's length? ;-)  Not complaining - it's a very high quality and 
informative discussion.

I'd be comfortable adopting whichever PRNGs numpy uses.  numpy has better 
brainpower to apply to "due diligence" in this area, and the discussion made 
clear too that they're acutely aware of that most users know next to nothing 
about the pathologies, so that the defaults have to be ignorance-resistant.

It's cute that you raised good questions about how "independent" PCG streams 
are, and that PCG's creator invented a new member of the family to address the 
pathologies your line of questioning uncovered.  No "proof" that the new member 
is robust, but lots of testing.  That appears to be as good as the state of art 
allows for now.

I had/have similar concerns about the Twister, but never pursued them.  Much 
like PCG, in fact, it mixes a simple generator with a more-elaborate 
permutation of the underlying generator's output sequence (which they call 
"tempering").

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<https://bugs.python.org/issue38767>
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