From murdoch@dunc@n @ending from gm@il@com  Wed Sep 19 14:43:26 2018
From: murdoch@dunc@n @ending from gm@il@com (Duncan Murdoch)
Date: Wed, 19 Sep 2018 08:43:26 -0400
Subject: [Rd] Bias in R's random integers?
In-Reply-To: <CAN_1p9wVX=AR8aYtC2LJo0bgN9cRW3XcbYJqnVHdCzA-QA1ceg@mail.gmail.com>
References: <CAN_1p9wVX=AR8aYtC2LJo0bgN9cRW3XcbYJqnVHdCzA-QA1ceg@mail.gmail.com>
Message-ID: <ffb74021-8d95-a820-8013-f0e51dc1a9b3@gmail.com>

On 18/09/2018 5:46 PM, Carl Boettiger wrote:
> Dear list,
> 
> It looks to me that R samples random integers using an intuitive but biased
> algorithm by going from a random number on [0,1) from the PRNG to a random
> integer, e.g.
> https://github.com/wch/r-source/blob/tags/R-3-5-1/src/main/RNG.c#L808
> 
> Many other languages use various rejection sampling approaches which
> provide an unbiased method for sampling, such as in Go, python, and others
> described here:  https://arxiv.org/abs/1805.10941 (I believe the biased
> algorithm currently used in R is also described there).  I'm not an expert
> in this area, but does it make sense for the R to adopt one of the unbiased
> random sample algorithms outlined there and used in other languages?  Would
> a patch providing such an algorithm be welcome? What concerns would need to
> be addressed first?
> 
> I believe this issue was also raised by Killie & Philip in
> http://r.789695.n4.nabble.com/Bug-in-sample-td4729483.html, and more
> recently in
> https://www.stat.berkeley.edu/~stark/Preprints/r-random-issues.pdf,
> pointing to the python implementation for comparison:
> https://github.com/statlab/cryptorandom/blob/master/cryptorandom/cryptorandom.py#L265

I think the analyses are correct, but I doubt if a change to the default 
is likely to be accepted as it would make it more difficult to reproduce 
older results.

On the other hand, a contribution of a new function like sample() but 
not suffering from the bias would be good.  The normal way to make such 
a contribution is in a user contributed package.

By the way, R code illustrating the bias is probably not very hard to 
put together.  I believe the bias manifests itself in sample() producing 
values with two different probabilities (instead of all equal 
probabilities).  Those may differ by as much as one part in 2^32.  It's 
very difficult to detect a probability difference that small, but if you 
define the partition of values into the high probability values vs the 
low probability values, you can probably detect the difference in a 
feasible simulation.

Duncan Murdoch



[Rd] Bias in R's random integers?
Duncan Murdoch