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Re: st: bootsrap random number use


From   Sergiy Radyakin <serjradyakin@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: bootsrap random number use
Date   Mon, 7 Oct 2013 12:52:40 -0400

On Mon, Oct 7, 2013 at 12:16 PM, philippe van kerm
<philippe.vankerm@ceps.lu> wrote:
>
>> -----Original Message-----
>> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
>> statalist@hsphsun2.harvard.edu] On Behalf Of Sergiy Radyakin
>> Sent: Monday, October 07, 2013 4:02 PM
>> To: statalist@hsphsun2.harvard.edu
>> Subject: Re: st: bootsrap random number use
>>
>> On Mon, Oct 7, 2013 at 6:48 AM, philippe van kerm
>> <philippe.vankerm@ceps.lu> wrote:
>> > It seems to me the -bsample- code is simply meant to avoid the
>> explicit loop over observations (and so is fast even with many
>> observations), but does not do extra magic otherwise. I would think the
>> second uniform() ensures that the bootstrap draw does not depend on the
>> initial sort order of the data.
>>
>> Dear Philippe, thank you for this addition, but I still don't get it:
>> how would the draws depend on the sort order of the data?
>
> Sergiy,
>
> I think it is because of the particular way -bsample- is coded. And in fact, my statement was inaccurate: it is a reproducibility issue.
>
> Internally -bsample- does
>         gen double `r' = int(uniform()*_N + 1)
>       gen double `w' = uniform()
>       sort `r' `w'
> The second variable (`w') ensures that the sort order is identical across repetitions for a given value of the seed (this would not be guaranteed otherwise).


Dear Philippe, I guess I understand now (with your explanation and the
following post from Bill Gould
http://blog.stata.com/2012/08/03/using-statas-random-number-generators-part-2-drawing-without-replacement/)
that the second random variable would ensure the results are
reproducible. However, collisions in `w' are still possible, though
waaay less likely because of its 'double' precision. It seems to me
the same result could have been achieved if the above quoted code was:
        gen double `r' = uniform()*_N + 1
       sort `r'
       replace `r'=int(`r')
but this code would use only one random number per observation.

Thank you, Sergiy Radyakin




>
> I convinced myself by repeating this code a few times:
>
>  clear
>  set seed 12345
>  set obs 1000
>  gen id = _n
>  generate ui = floor((_N)*runiform() + 1)
>  generate w = runiform()
>  sort ui
>  list id ui  in 1/10
>  sort ui w
>  list id ui  in 1/10
>
> Despite the -set seed- statement, the sort order -sort ui- is not identical across replications, while it is always the same after -sort ui w-.
>
> This is crucial to ensure reproducibility of -bsample- results.
>
>> Is there
>> such a problem with my model code? Note that I don't loop over
>> observations, I loop over -draws-. Performance is not an issue here,
>> but the amount of randomness is. Even if I can't recover the logic
>> behind the bootstrap, can I be absolutely confident that it will
>> require 2*N*k random numbers for k iterations? Or is it (N+1)*k?
>
> I think the different number of random numbers required by -bsample- and your code just reflects coding differences. It is not inherent to the bootstrap. I would guess you could code it with N random numbers, if that matters.
>
> Philippe
>
>> Thank you, Sergiy Radyakin
>>
>>
>> >
>> > Philippe
>> >
>> >> -----Original Message-----
>> >> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-
>> >> statalist@hsphsun2.harvard.edu] On Behalf Of Sergiy Radyakin
>> >> Sent: Saturday, October 05, 2013 1:15 AM
>> >> To: statalist@hsphsun2.harvard.edu
>> >> Subject: Re: st: bootsrap random number use
>> >>
>> >> On Fri, Oct 4, 2013 at 6:47 PM, Stas Kolenikov <skolenik@gmail.com>
>> >> wrote:
>> >> > As far as I remember looking at the -bsample- code, which I never
>> >> > understood, it also sorts the data this or that way when -expand-
>> ing
>> >> > the bootstrap frequencies.
>> >>
>> >> Yes, Stas, I also see the sorts, and yes, I also don't understand
>> what
>> >> it is doing
>> >> exactly there. My view on bootstrap is that it is doing sampling
>> with
>> >> replacement,
>> >>
>> http://en.wikipedia.org/wiki/Bootstrapping_%28statistics%29#Case_resamp
>> >> ling ,
>> >> so should be similar to the following minimal code:
>> >>
>> >> http://www.radyakin.org/statalist/2013100401/picksample.do
>> >>
>> >> which takes exactly N random numbers to create a subsample (with
>> >> replacement)
>> >> from the original sample of N observations. If Stata requires more
>> >> 'randomness', I
>> >> assume it is doing something more complicated, and I am curious to
>> >> know what is it.
>> >>
>> >> Thank you, Sergiy Radyakin
>> >>
>> >>
>> >>
>> >> >
>> >> > -- Stas Kolenikov, PhD, PStat (ASA, SSC)
>> >> > -- Senior Survey Statistician, Abt SRBI
>> >> > -- Opinions stated in this email are mine only, and do not reflect
>> >> the
>> >> > position of my employer
>> >> > -- http://stas.kolenikov.name
>> >> >
>> >> >
>> >> >
>> >> > On Fri, Oct 4, 2013 at 1:45 PM, Sergiy Radyakin
>> >> <serjradyakin@gmail.com> wrote:
>> >> >> Dear Statalist,
>> >> >>
>> >> >> suppose I want to bootsrap myself. For a dataset with 74
>> >> observations
>> >> >> to do two bootstrap iterations I would need to pick 2x74=148
>> random
>> >> >> numbers, but Stata picks 296. Why?
>> >> >>
>> >> >> Thank you, Sergiy Radyakin
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