[Rd] Bias in R's random integers?

[Duncan Murdoch]

An email today reminded me of this issue.  The other bug (fractional 
population sizes) was fixed quite a while ago, but this one still 
exists.  I've posted a bug report about it (PR#17494).

Duncan Murdoch

On 20/09/2018 11:15 AM, Duncan Murdoch wrote:
> On 20/09/2018 6:59 AM, Ralf Stubner wrote:
>> On 9/20/18 1:43 AM, Carl Boettiger wrote:
>>> For a well-tested C algorithm, based on my reading of Lemire, the unbiased
>>> "algorithm 3" in https://arxiv.org/abs/1805.10941 is part already of the C
>>> standard library in OpenBSD and macOS (as arc4random_uniform), and in the
>>> GNU standard library.  Lemire also provides C++ code in the appendix of his
>>> piece for both this and the faster "nearly divisionless" algorithm.
>>>
>>> It would be excellent if any R core members were interested in considering
>>> bindings to these algorithms as a patch, or might express expectations for
>>> how that patch would have to operate (e.g. re Duncan's comment about
>>> non-integer arguments to sample size).  Otherwise, an R package binding
>>> seems like a good starting point, but I'm not the right volunteer.
>> It is difficult to do this in a package, since R does not provide access
>> to the random bits generated by the RNG. Only a float in (0,1) is
>> available via unif_rand().
> 
> I believe it is safe to multiply the unif_rand() value by 2^32, and take
> the whole number part as an unsigned 32 bit integer.  Depending on the
> RNG in use, that will give at least 25 random bits.  (The low order bits
> are the questionable ones.  25 is just a guess, not a guarantee.)
> 
> However, if one is willing to use an external
>> RNG, it is of course possible. After reading about Lemire's work [1], I
>> had planned to integrate such an unbiased sampling scheme into the dqrng
>> package, which I have now started. [2]
>>
>> Using Duncan's example, the results look much better:
>>
>>> library(dqrng)
>>> m <- (2/5)*2^32
>>> y <- dqsample(m, 1000000, replace = TRUE)
>>> table(y %% 2)
>>
>>        0      1
>> 500252 499748
> 
> Another useful diagnostic is
> 
>     plot(density(y[y %% 2 == 0]))
> 
> Obviously that should give a more or less uniform density, but for
> values near m, the default sample() gives some nice pretty pictures of
> quite non-uniform densities.
> 
> By the way, there are actually quite a few examples of very large m
> besides m = (2/5)*2^32 where performance of sample() is noticeably bad.
> You'll see problems in y %% 2 for any integer a > 1 with m = 2/(1 + 2a)
> * 2^32, problems in y %% 3 for m = 3/(1 + 3a)*2^32 or m = 3/(2 +
> 3a)*2^32, etc.
> 
> So perhaps I'm starting to be convinced that the default sample() should
> be fixed.
> 
> Duncan Murdoch
> 
> 
>>
>> Currently I am taking the other interpretation of "truncated":
>>
>>> table(dqsample(2.5, 1000000, replace = TRUE))
>>
>>        0      1
>> 499894 500106
>>
>> I will adjust this to whatever is decided for base R.
>>
>>
>> However, there is currently neither long vector nor weighted sampling
>> support. And the performance without replacement is quite bad compared
>> to R's algorithm with hashing.
>>
>> cheerio
>> ralf
>>
>> [1] via http://www.pcg-random.org/posts/bounded-rands.html
>> [2] https://github.com/daqana/dqrng/tree/feature/sample
>>
>>
>>
>> ______________________________________________
>> R-devel using r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-devel
>>
>