Re: [R] bootstrap resampling - simplified

From: Jonathan P Daily <jdaily_at_usgs.gov>
Date: Wed, 02 Mar 2011 15:00:28 -0500

I apologize if I was not clear in my response. I only mentioned x1, x2 in my example, but I did not clarify that I also knew that P(x6 = 1 | x1..5 = 1) = 0 in the original request. I also see that if he meant that he wanted to sample with replacement from the set of sequences that sample(rep(1:20, 5), 20) is fine for generating said sequences. My interpretation was that the sequences themselves should be sampling with replacement until frequency hits 5, whereupon it is not replaced. Hence my suggestion of:

bigsamp <- sample(1:20, 100, T)
idx <- sort(unlist(sapply(1:20, function(x) which(bigsamp == x)[1:5])))[1:20]
samp <- bigsamp[idx]

I apologize for my lack of clarity, though after reading the original post I'm not sure which solution the OP was looking for.

Cheers,
Jon



Jonathan P. Daily
Technician - USGS Leetown Science Center 11649 Leetown Road
Kearneysville WV, 25430
(304) 724-4480
"Is the room still a room when its empty? Does the room,  the thing itself have purpose? Or do we, what's the word... imbue it."

Bert Gunter <gunter.berton_at_gene.com> wrote on 03/02/2011 02:42:40 PM:

> [image removed]
>
> Re: [R] bootstrap resampling - simplified
>
> Bert Gunter
>
> to:
>
> Jonathan P Daily
>
> 03/02/2011 02:42 PM
>
> Cc:
>
> "Vokey, John", r-help, r-help-bounces
>
> Folks:
>
> On Wed, Mar 2, 2011 at 10:32 AM, Jonathan P Daily <jdaily_at_usgs.gov>
wrote:
> > I will point out again that sampling a five-fold replicate of 1:20 is
not
> > the same as resampling with replacement,
>
> -- Correct. In sampling with replacement from 1:20 there is positive
> probability of getting all 1's or all 2's, etc. The poster
> specifically said that he wanted 0 probability of such results. So,
> obviously, the poster does NOT want to "sample with replacement from
> 1:20." What he does want (I think) is a re-sample of size n from the
> set of all **vectors** of length 20, each element of which is an
> integer from 1 to 20, and for which no individual values occur more
> than 5 times in the vector. Of course I'm just
> interpreting/paraphrasing the original post (if I got it right), but I
> think doing so makes the nature of the task clearer: one needs to find
> some way to sample with replacement from the space of all such
> **sequences**.
>
> I think it is now clear that one may do so by rejection sampling: i.e.
> sample with replacement from 1:20 and throw away any sequences that
> fail the at most 5 criterion. The sequences that remain are samples of
> size 1 from the population of sequences that satisfy the poster's
> criteria (in theory, anyway; this might tax a pseudo RNG in practice).
> A collection of n such sequences is a bootstrap sample from this
> population. I **think** that's what the poster wants -- and what
> others have already provided. However, maybe this clarifies why it
> works.
>
> If I have made any error in this, **Please** post a message pointing
> out my error. I sometimes get confused about this stuff, too.
>
> Cheers,
> Bert
>
>
>
>
>
> although I made an error in
> > reporting probabilities - the P(x2 = 1 | x1 = 1) = 4/99 and not 4/100.
> > When sampling with replacement, P(x2 = 1 | x1 = 1) = P(x2 = 1 | x1 !=
1) =
> > 1/20.
> > --------------------------------------
> > Jonathan P. Daily
> > Technician - USGS Leetown Science Center
> > 11649 Leetown Road
> > Kearneysville WV, 25430
> > (304) 724-4480
> > "Is the room still a room when its empty? Does the room,
> > the thing itself have purpose? Or do we, what's the word... imbue
it."
> > - Jubal Early, Firefly
> >
> > r-help-bounces_at_r-project.org wrote on 03/02/2011 01:05:01 PM:

> >
> >> [image removed]
> >>
> >> Re: [R] bootstrap resampling - simplified
> >>
> >> Vokey, John
> >>
> >> to:
> >>
> >> r-help
> >>
> >> 03/02/2011 01:07 PM
> >>
> >> Sent by:
> >>
> >> r-help-bounces_at_r-project.org
> >>
> >> On 2011-03-02, at 4:00 AM, r-help-request_at_r-project.org wrote:
> >>
> >> > Hello there,
> >> >
> >> > I have a problem concerning bootstrapping in R - especially
> >> focusing on the resampling part of it. I try to sum it up in a
> >> simplified way so that I would not confuse anybody.
> >> >
> >> > I have a small database consisting of 20 observations (basically
> >> numbers from 1 to 20, I mean: 1, 2, 3, 4, 5, ... 18, 19, 20).
> >> >
> >> > I would like to resample this database many times for the
> >> bootstrap process with the following conditions. Firstly, every
> >> resampled database should also include 20 observations. Secondly,
> >> when selecting a number from the above-mentioned 20 numbers, you can
> >> do this selection with replacement. The difficult part comes now:
> >> one number can be selected only maximum 5 times. In order to make
> >> this clear I show you a couple of examples. So the resampled
> >> databases might be like the following ones:
> >> >
> >> > (1st database) 1,2,1,2,1,2,1,2,1,2,3,3,3,3,3,4,4,4,4,4
> >> > 4 different numbers are chosen (1, 2, 3, 4), each selected - for
> >> the maximum possible - 5 times.
> >> >
> >> > (2nd database) 1,8,8,6,8,8,8,2,3,4,5,6,6,6,6,7,19,1,1,1
> >> > Two numbers - 8 and 6 - selected 5 times (the maximum possible
> >> times), number 1 selected 4 times, the others selected less than 4
> > times.
> >> >
> >> > (3rd database) 1,1,2,2,3,3,4,4,9,9,9,10,10,13,10,9,3,9,2,1
> >> > Number 9 chosen for the maximum possible 5 times, number 10, 3, 2,
> >> 1 chosen for 3 times, number 4 selected twice and number 13
selectedonly
> > once.
> >> >
> >> > ...
> >> >
> >> > Anybody knows how to implement my "tricky" condition into one of
> >> the R functions - that one number can be selected only 5 times at
> >> most? Are 'boot' and 'bootstrap' packages capable of managing this?
> >> I guess they are, I just couldn't figure it out yet...
> >> >
> >> > Thanks very much! Best regards,
> >> > Laszlo Bodnar
> >>
> >> Laszlo,
> >> Create a vector consisting of 5 of each number. Then, for each
> >> sample, scramble the order of the items in the vector, and select
> >> the first 20.
> >>
> >>
> >> --
> >> Please avoid sending me Word or PowerPoint attachments.
> >> See <http://www.gnu.org/philosophy/no-word-attachments.html>
> >>
> >> -Dr. John R. Vokey
> >>
> >> ______________________________________________
> >> R-help_at_r-project.org mailing list
> >> https://stat.ethz.ch/mailman/listinfo/r-help
> >> PLEASE do read the posting guide
> > http://www.R-project.org/posting-guide.html
> >> and provide commented, minimal, self-contained, reproducible code.
> >
> > ______________________________________________
> > R-help_at_r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
> >
>
>
>
> --
> Bert Gunter
> Genentech Nonclinical Biostatistics
> 467-7374
> http://devo.gene.com/groups/devo/depts/ncb/home.shtml



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