Example for issues with 'naive' parallel seeding

[kkmann]

Dear all,

Reading through https://www.jottr.org/2020/09/22/push-for-statistical-sound-rng/ I realized that neither in the article nor in any of the references an actual counterexample to using 'naive' parallel seeding is given. I am refering to the code example given in the article using the loop index as seed:

library(parallel)
cl <- makeCluster(4)
y <- parLapply(cl, 1:10, function(i) {
  set.seed(i)
  runif(n = 5)
})
stopCluster(cl)

Is anyone aware of a reproducible example where this leads to practical issues that I could showcase with some summary statistics?

[kkmann]

Tagging @rstub as well, https://github.com/daqana/dqrng does a simple correlation test. Not sure what it shows though - in my experiments this also works for the default Mersenne twister

n <- 1e7
set.seed(1)
u1 <- runif(n)
set.seed(2)
u2 <- runif(n)
cor(u1, u2)
#> 3.653225e-05

[rstub]

Unfortunately I don't have a good example where "poor man's parallel RNG" breaks. The correlation being negligible in these cases is a necessary but not a sufficient condition.