Re: [R] Bug : Autocorrelation in sample drawn from stats::rnorm (hmh)
Nope.
This IS a bug:
_*The negative auto-correlation mostly disappear when I randomize small
samples using the R function '*__*sample*__*'.*_
Please check thoroughly the code of the 1st mail I sent, there should be
no difference between the two R functions I wrote to illustrate the bug.
The two functions that should produce the same output if there would be
no bug are 'DistributionAutocorrelation_Unexpected' and
'DistributionAutocorrelation_Expected'.
_/Please take the time to compare there output!!/_
The finite-sample bias in the sample autocorrelation coefficient you
mention should affect them in the same manner. This bias is not the only
phenomenon at work, *_there is ALSO as BUG !_*
Thanks
The first mail I sent is below :
_ _ _
Hi,
I just noticed the following bug:
When we draw a random sample using the function stats::rnorm, there
should be not auto-correlation in the sample. But their is some
auto-correlation _when the sample that is drawn is small_.
I describe the problem using two functions:
DistributionAutocorrelation_Unexpected which as the wrong behavior :
_when drawing some small samples using rnorm, there is generally a
strong negative auto-correlation in the sample_.
and
DistributionAutocorrelation_Expected which illustrate the expected behavior
*Unexpected : *
DistributionAutocorrelation_Unexpected = function(SampleSize){
Cor = NULL
for(repetition in 1:1e5){
X = rnorm(SampleSize)
Cor[repetition] = cor(X[-1],X[-length(X)])
}
return(Cor)
}
par(mfrow=c(3,3))
for(SampleSize_ in c(4,5,6,7,8,10,15,20,50)){
hist(DistributionAutocorrelation_Unexpected(SampleSize_),col='grey',main=paste0('SampleSize=',SampleSize_))
; abline(v=0,col=2)
}
output:
*Expected**:*
DistributionAutocorrelation_Expected = function(SampleSize){
Cor = NULL
for(repetition in 1:1e5){
X = rnorm(SampleSize)
* Cor[repetition] = cor(sample(X[-1]),sample(X[-length(X)]))*
}
return(Cor)
}
par(mfrow=c(3,3))
for(SampleSize_ in c(4,5,6,7,8,10,15,20,50)){
hist(DistributionAutocorrelation_Expected(SampleSize_),col='grey',main=paste0('SampleSize=',SampleSize_))
; abline(v=0,col=2)
}
Some more information you might need:
packageDescription("stats")
Package: stats
Version: 3.5.1
Priority: base
Title: The R Stats Package
Author: R Core Team and contributors worldwide
Maintainer: R Core Team
Description: R statistical functions.
License: Part of R 3.5.1
Imports: utils, grDevices, graphics
Suggests: MASS, Matrix, SuppDists, methods, stats4
NeedsCompilation: yes
Built: R 3.5.1; x86_64-pc-linux-gnu; 2018-07-03 02:12:37 UTC; unix
Thanks for correcting that.
fill free to ask any further information you would need.
cheers,
hugo
On 05/10/2018 09:58, Annaert Jan wrote:
On 05/10/2018, 09:45, "R-help on behalf of hmh" wrote:
Hi,
Thanks William for this fast answer, and sorry for sending the 1st mail
to r-help instead to r-devel.
I noticed that bug while I was simulating many small random walks using
c(0,cumsum(rnorm(10))). Then the negative auto-correlation was inducing
a muchsmaller space visited by the random walks than expected if there
would be no auto-correlation in the samples.
The code I provided and you optimized was only provided to illustrated
and investigate that bug.
It is really worrying that most of the R distributions are affected by
this bug
What I did should have been one of the first check done for _*each*_
distributions by the developers of these functions !
And if as you suggested this is a "tolerated" _error_ of the algorithm,
I do think this is a bad choice, but any way, this should have been
mentioned in the documentations of the functions !!
cheers,
hugo
This is not a bug. You have simply rediscovered the finite-sample bias in the sample autocorrelation coefficient, known at least since
Kendall, M. G. (1954). Note on bias in the estimation of autocorrelation.
Biometrika, 41(3-4), 403-404.
The bias is approximately -1/T, with T sample size, which explains why it seems
to disappear in the larger sample sizes you consider.
Jan
--
- no title specified
Hugo Mathé-Hubert
ATER
Laboratoire Interdisciplinaire des Environnements Continentaux (LIEC)
UMR 7360 CNRS - Bât IBISE
Université de Lorraine - UFR SciFA
8, Rue du Général Delestraint
F-57070 METZ
+33(0)9 77 21 66 66
- - - - - - - - - - - - - - - - - -
Les réflexions naissent dans les doutes et meurent dans les certitudes.
Les doutes sont donc un signe de force et les certitudes un signe de
faiblesse. La plupart des gens sont pourtant certains du contraire.
- - - - - - - - - - - - - - - - - -
Thoughts appear from doubts and die in convictions. Therefore, doubts
are an indication of strength and convictions an indication of weakness.
Yet, most people believe the opposite.
Re: [R] Bug : Autocorrelation in sample drawn from stats::rnorm (hmh)
I got it ! thanks and sorry for annoying you with that. have a nice day, hugo On 05/10/2018 11:16, Deepayan Sarkar wrote: > On Fri, Oct 5, 2018 at 2:07 PM hmh wrote: >> On 05/10/2018 10:28, Annaert Jan wrote: >>> you discard any time series structure; >> But that is PRECISELY what a call a bug: >> There should not be any "time series structure" in the output or rnorm, >> runif and so on but there is one. >> >> rnorm(N,0,1) >> should give on average the same output as >> sample(rnorm(N,0,1)) > Agreed, but that is not what your code is testing. You seem to think > that something much more specific should be true; namely, > > X[1:10] ~ iid normal, then > > cor(X[1:9], X[2:10]) > > and > > cor(sample(X[-1]), sample(X[-10])) > > should have the same distribution. This is not at all obvious, and in > fact not true. > > Please check the reference you have been pointed to. Here is a related > article in the same volume: > > https://www.jstor.org/stable/2332719 > > -Deepayan > > >> Which is not the case. rnorm(N,0,1) should draw INDEPENDENT samples i.e. >> without time series structure ! >> >> >> -- >> - no title specified >> >> Hugo Mathé-Hubert >> >> ATER >> >> Laboratoire Interdisciplinaire des Environnements Continentaux (LIEC) >> >> UMR 7360 CNRS - Bât IBISE >> >> Université de Lorraine - UFR SciFA >> >> 8, Rue du Général Delestraint >> >> F-57070 METZ >> >> +33(0)9 77 21 66 66 >> - - - - - - - - - - - - - - - - - - >> Les réflexions naissent dans les doutes et meurent dans les certitudes. >> Les doutes sont donc un signe de force et les certitudes un signe de >> faiblesse. La plupart des gens sont pourtant certains du contraire. >> - - - - - - - - - - - - - - - - - - >> Thoughts appear from doubts and die in convictions. Therefore, doubts >> are an indication of strength and convictions an indication of weakness. >> Yet, most people believe the opposite. >> >> >> [[alternative HTML version deleted]] >> >> __ >> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >> 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. -- - no title specified Hugo Mathé-Hubert ATER Laboratoire Interdisciplinaire des Environnements Continentaux (LIEC) UMR 7360 CNRS - Bât IBISE Université de Lorraine - UFR SciFA 8, Rue du Général Delestraint F-57070 METZ +33(0)9 77 21 66 66 - - - - - - - - - - - - - - - - - - Les réflexions naissent dans les doutes et meurent dans les certitudes. Les doutes sont donc un signe de force et les certitudes un signe de faiblesse. La plupart des gens sont pourtant certains du contraire. - - - - - - - - - - - - - - - - - - Thoughts appear from doubts and die in convictions. Therefore, doubts are an indication of strength and convictions an indication of weakness. Yet, most people believe the opposite. [[alternative HTML version deleted]] __ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
Re: [R] Bug : Autocorrelation in sample drawn from stats::rnorm (hmh)
On Fri, Oct 5, 2018 at 2:07 PM hmh wrote: > > On 05/10/2018 10:28, Annaert Jan wrote: > > you discard any time series structure; > But that is PRECISELY what a call a bug: > There should not be any "time series structure" in the output or rnorm, > runif and so on but there is one. > > rnorm(N,0,1) > should give on average the same output as > sample(rnorm(N,0,1)) Agreed, but that is not what your code is testing. You seem to think that something much more specific should be true; namely, X[1:10] ~ iid normal, then cor(X[1:9], X[2:10]) and cor(sample(X[-1]), sample(X[-10])) should have the same distribution. This is not at all obvious, and in fact not true. Please check the reference you have been pointed to. Here is a related article in the same volume: https://www.jstor.org/stable/2332719 -Deepayan > Which is not the case. rnorm(N,0,1) should draw INDEPENDENT samples i.e. > without time series structure ! > > > -- > - no title specified > > Hugo Mathé-Hubert > > ATER > > Laboratoire Interdisciplinaire des Environnements Continentaux (LIEC) > > UMR 7360 CNRS - Bât IBISE > > Université de Lorraine - UFR SciFA > > 8, Rue du Général Delestraint > > F-57070 METZ > > +33(0)9 77 21 66 66 > - - - - - - - - - - - - - - - - - - > Les réflexions naissent dans les doutes et meurent dans les certitudes. > Les doutes sont donc un signe de force et les certitudes un signe de > faiblesse. La plupart des gens sont pourtant certains du contraire. > - - - - - - - - - - - - - - - - - - > Thoughts appear from doubts and die in convictions. Therefore, doubts > are an indication of strength and convictions an indication of weakness. > Yet, most people believe the opposite. > > > [[alternative HTML version deleted]] > > __ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > 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 -- To UNSUBSCRIBE and more, see 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.
Re: [R] Bug : Autocorrelation in sample drawn from stats::rnorm (hmh)
On 05/10/2018 10:28, Annaert Jan wrote: > you discard any time series structure; But that is PRECISELY what a call a bug: There should not be any "time series structure" in the output or rnorm, runif and so on but there is one. rnorm(N,0,1) should give on average the same output as sample(rnorm(N,0,1)) Which is not the case. rnorm(N,0,1) should draw INDEPENDENT samples i.e. without time series structure ! -- - no title specified Hugo Mathé-Hubert ATER Laboratoire Interdisciplinaire des Environnements Continentaux (LIEC) UMR 7360 CNRS - Bât IBISE Université de Lorraine - UFR SciFA 8, Rue du Général Delestraint F-57070 METZ +33(0)9 77 21 66 66 - - - - - - - - - - - - - - - - - - Les réflexions naissent dans les doutes et meurent dans les certitudes. Les doutes sont donc un signe de force et les certitudes un signe de faiblesse. La plupart des gens sont pourtant certains du contraire. - - - - - - - - - - - - - - - - - - Thoughts appear from doubts and die in convictions. Therefore, doubts are an indication of strength and convictions an indication of weakness. Yet, most people believe the opposite. [[alternative HTML version deleted]] __ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
Re: [R] Bug : Autocorrelation in sample drawn from stats::rnorm (hmh)
On 05/10/2018, 09:45, "R-help on behalf of hmh" wrote: Hi, Thanks William for this fast answer, and sorry for sending the 1st mail to r-help instead to r-devel. I noticed that bug while I was simulating many small random walks using c(0,cumsum(rnorm(10))). Then the negative auto-correlation was inducing a muchsmaller space visited by the random walks than expected if there would be no auto-correlation in the samples. The code I provided and you optimized was only provided to illustrated and investigate that bug. It is really worrying that most of the R distributions are affected by this bug What I did should have been one of the first check done for _*each*_ distributions by the developers of these functions ! And if as you suggested this is a "tolerated" _error_ of the algorithm, I do think this is a bad choice, but any way, this should have been mentioned in the documentations of the functions !! cheers, hugo This is not a bug. You have simply rediscovered the finite-sample bias in the sample autocorrelation coefficient, known at least since Kendall, M. G. (1954). Note on bias in the estimation of autocorrelation. Biometrika, 41(3-4), 403-404. The bias is approximately -1/T, with T sample size, which explains why it seems to disappear in the larger sample sizes you consider. Jan __ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see 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.
Re: [R] Bug : Autocorrelation in sample drawn from stats::rnorm (hmh)
Hi,
Thanks William for this fast answer, and sorry for sending the 1st mail
to r-help instead to r-devel.
I noticed that bug while I was simulating many small random walks using
c(0,cumsum(rnorm(10))). Then the negative auto-correlation was inducing
a muchsmaller space visited by the random walks than expected if there
would be no auto-correlation in the samples.
The code I provided and you optimized was only provided to illustrated
and investigate that bug.
It is really worrying that most of the R distributions are affected by
this bug
What I did should have been one of the first check done for _*each*_
distributions by the developers of these functions !
And if as you suggested this is a "tolerated" _error_ of the algorithm,
I do think this is a bad choice, but any way, this should have been
mentioned in the documentations of the functions !!
cheers,
hugo
On 05/10/2018 01:52, William Bell wrote:
> Hi Hugo,
>
> I've been able to replicate your bug, including for other
> distributions (runif, rexp, rgamma, etc) which shouldn't be surprising
> since they're probably all drawing from the same pseudo-random number
> generator. Interestingly, it does not seem to depend on the choice of
> seed, I am not sure why that is the case.
>
> I'll point out first of all that the R-devel mailing list is perhaps
> better suited for this query, I'm fairly sure we're supposed to direct
> bug reports, etc there.
>
> It is possible this is a known quantity but is tolerated, I could
> think of many reasons why that might be the case, not least of which
> being that as far as I know, the vast majority of Monte Carlo methods
> involve >>40 trials (which seems to be enough for the effect to
> disappear), with the possible exception of procedures for testing the
> power of statistical tests on small samples?
>
> There might be more to be said, but I thought I'd just add what I
> could from playing around with it a little bit.
>
> For anyone who wishes to give it a try, I suggest this implementation
> of the autocorrelation tester which is about 80 times faster:
>
> DistributionAutocorrelation_new <- function(SampleSize){
> Cor <- replicate(1e5, function() {X <- rnorm(SampleSize)
> return(cor(X[-1], X[-length(X)]))})
> return(Cor)
> }
>
> I have the same Stats package version installed.
>
> - (Thomas) William Bell
> Hons BSc Candidate (Biology and Mathematics)
> BA Candidate (Philosophy)
> McMaster University
>
> # Hi,
> #
> #
> # I just noticed the following bug:
> #
> # When we draw a random sample using the function stats::rnorm, there
> # should be not auto-correlation in the sample. But their is some
> # auto-correlation _when the sample that is drawn is small_.
> #
> # I describe the problem using two functions:
> #
> # DistributionAutocorrelation_Unexpected which as the wrong behavior :
> # _when drawing some small samples using rnorm, there is generally a
> # strong negative auto-correlation in the sample_.
> #
> # and
> #
> # DistributionAutocorrelation_Expected which illustrate the expected
> behavior
> #
> #
> #
> # *Unexpected : *
> #
> # DistributionAutocorrelation_Unexpected = function(SampleSize){
> # Cor = NULL
> # for(repetition in 1:1e5){
> # X = rnorm(SampleSize)
> # Cor[repetition] = cor(X[-1],X[-length(X)])
> # }
> # return(Cor)
> # }
> #
> # par(mfrow=c(3,3))
> # for(SampleSize_ in c(4,5,6,7,8,10,15,20,50)){
> #
> hist(DistributionAutocorrelation_Unexpected(SampleSize_),col='grey',main=paste0('SampleSize=',SampleSize_))
>
>
> # ; abline(v=0,col=2)
> # }
> #
> # output:
> #
> #
> # *Expected**:*
> #
> # DistributionAutocorrelation_Expected = function(SampleSize){
> # Cor = NULL
> # for(repetition in 1:1e5){
> # X = rnorm(SampleSize)
> # * Cor[repetition] = cor(sample(X[-1]),sample(X[-length(X)]))*
> # }
> # return(Cor)
> # }
> #
> # par(mfrow=c(3,3))
> # for(SampleSize_ in c(4,5,6,7,8,10,15,20,50)){
> #
> hist(DistributionAutocorrelation_Expected(SampleSize_),col='grey',main=paste0('SampleSize=',SampleSize_))
>
>
> # ; abline(v=0,col=2)
> # }
> #
> #
> #
> #
> # Some more information you might need:
> #
> #
> # packageDescription("stats")
> # Package: stats
> # Version: 3.5.1
> # Priority: base
> # Title: The R Stats Package
> # Author: R Core Team and contributors worldwide
> # Maintainer: R Core Team
> # Description: R statistical functions.
> # License: Part of R 3.5.1
> # Imports: utils, grDevices, graphics
> # Suggests: MASS, Matrix, SuppDists, methods, stats4
> # NeedsCompilation: yes
> # Built: R 3.5.1; x86_64-pc-linux-gnu; 2018-07-03 02:12:37 UTC; unix
> #
> # Thanks for correcting that.
> #
> # fill free to ask any further information you would need.
> #
> # cheers,
> #
> # hugo
> #
> #
> # --
> # - no title specified
> #
> # Hugo Mathé-Hubert
> #
> # ATER
> #
> # Laboratoire Interdisciplinaire des Environnements Continentaux (LIEC)
> #
> # UMR 7360
Re: [R] Bug : Autocorrelation in sample drawn from stats::rnorm (hmh)
Hi Hugo,
I've been able to replicate your bug, including for other distributions (runif,
rexp, rgamma, etc) which shouldn't be surprising since they're probably all
drawing from the same pseudo-random number generator. Interestingly, it does
not seem to depend on the choice of seed, I am not sure why that is the case.
I'll point out first of all that the R-devel mailing list is perhaps better
suited for this query, I'm fairly sure we're supposed to direct bug reports,
etc there.
It is possible this is a known quantity but is tolerated, I could think of many
reasons why that might be the case, not least of which being that as far as I
know, the vast majority of Monte Carlo methods involve >>40 trials (which seems
to be enough for the effect to disappear), with the possible exception of
procedures for testing the power of statistical tests on small samples?
There might be more to be said, but I thought I'd just add what I could from
playing around with it a little bit.
For anyone who wishes to give it a try, I suggest this implementation of the
autocorrelation tester which is about 80 times faster:
DistributionAutocorrelation_new <- function(SampleSize){
Cor <- replicate(1e5, function() {X <- rnorm(SampleSize)
return(cor(X[-1], X[-length(X)]))}) return(Cor)}
I have the same Stats package version installed.
- (Thomas) William BellHons BSc Candidate (Biology and Mathematics)BA Candidate
(Philosophy)McMaster University
# Hi,# # # I just noticed the following bug:# # When we draw a random
sample using the function stats::rnorm, there # should be not auto-correlation
in the sample. But their is some # auto-correlation _when the sample that is
drawn is small_.# # I describe the problem using two functions:# #
DistributionAutocorrelation_Unexpected which as the wrong behavior : # _when
drawing some small samples using rnorm, there is generally a # strong negative
auto-correlation in the sample_.# # and# # DistributionAutocorrelation_Expected
which illustrate the expected behavior# # # # *Unexpected : *# #
DistributionAutocorrelation_Unexpected = function(SampleSize){# Cor = NULL#
for(repetition in 1:1e5){# X = rnorm(SampleSize)#
Cor[repetition] = cor(X[-1],X[-length(X)])# }# return(Cor)# }# #
par(mfrow=c(3,3))# for(SampleSize_ in c(4,5,6,7,8,10,15,20,50)){#
hist(DistributionAutocorrelation_Unexpected(SampleSize_),col='grey',main=paste0('SampleSize=',SampleSize_))
# ; abline(v=0,col=2)# }# # output:# # # *Expected**:*# #
DistributionAutocorrelation_Expected = function(SampleSize){# Cor = NULL#
for(repetition in 1:1e5){# X = rnorm(SampleSize)# *
Cor[repetition] = cor(sample(X[-1]),sample(X[-length(X)]))*# }#
return(Cor)# }# # par(mfrow=c(3,3))# for(SampleSize_ in
c(4,5,6,7,8,10,15,20,50)){#
hist(DistributionAutocorrelation_Expected(SampleSize_),col='grey',main=paste0('SampleSize=',SampleSize_))
# ; abline(v=0,col=2)# }# # # # # Some more information you might need:# #
# packageDescription("stats")# Package: stats# Version: 3.5.1# Priority:
base# Title: The R Stats Package# Author: R Core Team and contributors
worldwide# Maintainer: R Core Team # Description: R
statistical functions.# License: Part of R 3.5.1# Imports: utils, grDevices,
graphics# Suggests: MASS, Matrix, SuppDists, methods, stats4# NeedsCompilation:
yes# Built: R 3.5.1; x86_64-pc-linux-gnu; 2018-07-03 02:12:37 UTC; unix# #
Thanks for correcting that.# # fill free to ask any further information you
would need.# # cheers,# # hugo# # # -- # - no title specified# # Hugo
Mathé-Hubert# # ATER# # Laboratoire Interdisciplinaire des Environnements
Continentaux (LIEC)# # UMR 7360 CNRS - Bât IBISE# # Université de Lorraine -
UFR SciFA# # 8, Rue du Général Delestraint# # F-57070 METZ# # +33(0)9 77 21 66
66# - - - - - - - - - - - - - - - - - -# Les réflexions naissent dans les
doutes et meurent dans les certitudes. # Les doutes sont donc un signe de force
et les certitudes un signe de # faiblesse. La plupart des gens sont pourtant
certains du contraire.# - - - - - - - - - - - - - - - - - -# Thoughts appear
from doubts and die in convictions. Therefore, doubts # are an indication of
strength and convictions an indication of weakness. # Yet, most people believe
the opposite.
[[alternative HTML version deleted]]
__
R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see
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.
