Puzzled by the behaviour of rbinom().

Rolf,

On Jul 29, 2022, at 4:36 PM, Rolf Turner <r.turner at auckland.ac.nz> wrote:

In a certain arcane context I wanted to look at the result of
applying rbinom() to two versions of the probability argument,
the versions differing in only a small number (three) of entries.

I thought that if I called set.seed() (with the same argument) prior to
each call to rbinom(), I would get results that differed only where the
probabilities differed. Most of the time this appears to be true:

set.seed(17) # Or any other seed, in my experience.
p0 <- runif(147)
p1 <- p0
p1[c(26,65,131)] <- 0.5
set.seed(42)
r0 <- rbinom(147,1000,p0)
set.seed(42)
r1 <- rbinom(147,1000,p1)

[rest deleted]

The fillip is that rbinom may use a variable number of draws from a uniform to generate the binomial.

You can read the  Kachitvichyanukul and Schmeiser article or hunt through the code to see what it does, but brute force exploration will give you a sense:

set.seed(1)
u1000 <- runif(1000)
res <-
  sapply(u1000,
         function(pr){
           set.seed(1)
           rbinom(1,1000,pr)
           u_next <- runif(1)
           j <- match(u_next, u1000)
           c( i, j-1, pr)} )

table(res[2,]) # how many draws
range(res[3, res[2,] == 2]) # range when 2 draws
plot(res[2,], res[3,])

Evidently, tails of `pr' only need one draw, but the interior needs two.

So my guess is that the changes you made shifted the RNG stream.

I guess you need to reset the seed for each trial.

---

FWIW, I tried your p.weird example, but did not get the same results as you showed. Only elements 26, 65, and 131 differed.


Note that for me:

RNGkind()

[1] "Mersenne-Twister" "Inversion"        "Rejection"

sessionInfo()

R version 4.2.0 (2022-04-22)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Monterey 12.4

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.2-arm64/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

loaded via a namespace (and not attached):
[1] compiler_4.2.0 tools_4.2.0

HTH,
Chuck