[Rd] bias issue in sample() (PR 17494)

[Kirill Müller]

Gabe


As mentioned on Twitter, I think the following behavior should be fixed 
as part of the upcoming changes:

R.version.string
## [1] "R Under development (unstable) (2019-02-25 r76160)"
.Machine$double.digits
## [1] 53
set.seed(123)
RNGkind()
## [1] "Mersenne-Twister" "Inversion"        "Rejection"
length(table(runif(1e6)))
## [1] 999863

I don't expect any collisions when using Mersenne-Twister to generate a 
million floating point values. I'm not sure what causes this behavior, 
but it's documented in ?Random:

"Do not rely on randomness of low-order bits from RNGs. Most of the 
supplied uniform generators return 32-bit integer values that are 
converted to doubles, so they take at most 2^32 distinct values and long 
runs will return duplicated values (Wichmann-Hill is the exception, and 
all give at least 30 varying bits.)"

The "Wichman-Hill" bit is interesting:

RNGkind("Wichmann-Hill")
length(table(runif(1e6)))
## [1] 1000000
length(table(runif(1e6)))
## [1] 1000000

Mersenne-Twister has a much much larger periodicity than Wichmann-Hill, 
it would be great to see the above behavior also for Mersenne-Twister. 
Thanks for considering.


Best regards

Kirill


On 20.02.19 08:01, Gabriel Becker wrote:
> Luke,
>
> I'm happy to help with this. Its great to see this get tackled (I've cc'ed
> Kelli Ottoboni who helped flag this issue).
>
> I can prepare a patch for the RNGkind related stuff and the doc update.
>
> As for ???, what are your (and others') thoughts about the possibility of
> a) a reproducibility API which takes either an R version (or maybe
> alternatively a date) and sets the RNGkind to the default for that
> version/date, and/or b) that sessionInfo be modified to capture (and
> display) the RNGkind in effect.
>
> Best,
> ~G
>
>
> On Tue, Feb 19, 2019 at 11:52 AM Tierney, Luke <luke-tierney using uiowa.edu>
> wrote:
>
>> Before the next release we really should to sort out the bias issue in
>> sample() reported by Ottoboni and Stark in
>> https://www.stat.berkeley.edu/~stark/Preprints/r-random-issues.pdf and
>> filed aa a bug report by Duncan Murdoch at
>> https://bugs.r-project.org/bugzilla/show_bug.cgi?id=17494.
>>
>> Here are two examples of bad behavior through current R-devel:
>>
>>       set.seed(123)
>>       m <- (2/5) * 2^32
>>       x <- sample(m, 1000000, replace = TRUE)
>>       table(x %% 2, x > m / 2)
>>       ##
>>       ##    FALSE   TRUE
>>       ## 0 300620 198792
>>       ## 1 200196 300392
>>
>>       table(sample(2/7 * 2^32, 1000000, replace = TRUE) %% 2)
>>       ##
>>       ##      0      1
>>       ## 429054 570946
>>
>> I committed a modification to R_unif_index to address this by
>> generating random bits (blocks of 16) and rejection sampling, but for
>> now this is only enabled if the environment variable R_NEW_SAMPLE is
>> set before the first call.
>>
>> Some things still needed:
>>
>> - someone to look over the change and see if there are any issues
>> - adjustment of RNGkind to allowing the old behavior to be selected
>> - make the new behavior the default
>> - adjust documentation
>> - ???
>>
>> Unfortunately I don't have enough free cycles to do this, but I can
>> help if someone else can take the lead.
>>
>> There are two other places I found that might suffer from the same
>> issue, in walker_ProbSampleReplace (pointed out bu O & S) and in
>> src/nmath/wilcox.c.  Both can be addressed by using R_unif_index. I
>> have done that for walker_ProbSampleReplace, but the wilcox change
>> might need adjusting to support the standalone math library and I
>> don't feel confident enough I'd get that right.
>>
>> Best,
>>
>> luke
>>
>>
>> --
>> Luke Tierney
>> Ralph E. Wareham Professor of Mathematical Sciences
>> University of Iowa                  Phone:             319-335-3386
>> Department of Statistics and        Fax:               319-335-3017
>>      Actuarial Science
>> 241 Schaeffer Hall                  email:   luke-tierney using uiowa.edu
>> Iowa City, IA 52242                 WWW:  http://www.stat.uiowa.edu
>>
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