Folks: On Wed, Mar 2, 2011 at 10:32 AM, Jonathan P Daily <jda...@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-boun...@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-boun...@r-project.org >> >> On 2011-03-02, at 4:00 AM, r-help-requ...@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@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@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 ______________________________________________ R-help@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.