From @t@rk @ending from @t@t@berkeley@edu  Wed Sep 19 18:09:09 2018
From: @t@rk @ending from @t@t@berkeley@edu (Philip B. Stark)
Date: Wed, 19 Sep 2018 09:09:09 -0700
Subject: [Rd] Bias in R's random integers?
In-Reply-To: <ece52410-ddb2-2198-9291-201475d3f46e@gmail.com>
References: <CAN_1p9wVX=AR8aYtC2LJo0bgN9cRW3XcbYJqnVHdCzA-QA1ceg@mail.gmail.com>
 <ffb74021-8d95-a820-8013-f0e51dc1a9b3@gmail.com>
 <CALEXWq3booRRTSYvYqcjV7qPZGOC1oh5o45b5o=J2ypQi5s-ag@mail.gmail.com>
 <ece52410-ddb2-2198-9291-201475d3f46e@gmail.com>
Message-ID: <CAA7KnHHEejYVn8NtKrY1KuKcJUq8n4LoJSDx9BZv-LJyC=r9yQ@mail.gmail.com>

The 53 bits only encode at most 2^{32} possible values, because the source
of the float is the output of a 32-bit PRNG (the obsolete version of MT).
53 bits isn't the relevant number here.

The selection ratios can get close to 2. Computer scientists don't do it
the way R does, for a reason.

Regards,
Philip

On Wed, Sep 19, 2018 at 9:05 AM Duncan Murdoch <murdoch.duncan at gmail.com>
wrote:

> On 19/09/2018 9:09 AM, I?aki Ucar wrote:
> > El mi?., 19 sept. 2018 a las 14:43, Duncan Murdoch
> > (<murdoch.duncan at gmail.com>) escribi?:
> >>
> >> 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
> >
> > According to Kellie and Philip, in the attachment of the thread
> > referenced by Carl, "The maximum ratio of selection probabilities can
> > get as large as 1.5 if n is just below 2^31".
>
> Sorry, I didn't write very well.  I meant to say that the difference in
> probabilities would be 2^-32, not that the ratio of probabilities would
> be 1 + 2^-32.
>
> By the way, I don't see the statement giving the ratio as 1.5, but maybe
> I was looking in the wrong place.  In Theorem 1 of the paper I was
> looking in the ratio was "1 + m 2^{-w + 1}".  In that formula m is your
> n.  If it is near 2^31, R uses w = 57 random bits, so the ratio would be
> very, very small (one part in 2^25).
>
> The worst case for R would happen when m  is just below  2^25, where w
> is at least 31 for the default generators.  In that case the ratio could
> be about 1.03.
>
> Duncan Murdoch
>


-- 
Philip B. Stark | Associate Dean, Mathematical and Physical Sciences |
Professor,  Department of Statistics |
University of California
Berkeley, CA 94720-3860 | 510-394-5077 | statistics.berkeley.edu/~stark |
@philipbstark

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[Rd] Bias in R's random integers?
Philip B. Stark