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 <r-c...@r-project.org># 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.
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