Variable probability Bernoulli outcomes – Fast and Slow

I am working on a project that requires the generation of Bernoulli outcomes. Typically, I would go about this using the built in sample() function like so:

sample(1:0,n,prob=c(p,1-p),replace=TRUE)

This works great and is fast, even for large n. Problem is, I want to generate each sample with its own unique probability. Seems straight forward enough, I just wrapped the function and vectorized to allow the passing of a vector of p.

binomial_sampler<-function(p){
  return(sample(1:0,1,prob=c(p,1-p)))
}
bs<-Vectorize(binomial_sampler)

Naming this function bs() turned out to be rather prophetic. Nevertheless, I can call this function by passing my unique vector of outcome probabilities. And indeed I get the result I’m looking for.

bs(my_p_vec)

Problem is, this turns out to be very slow. It would seem that there is quite a bit of overhead to calling sample() for one sample at a time. R’s RNGs are very fast for generating many iid samples, so I started thinking like my old c++ programming self and tried a different approach.

Nbs<-function(p)
{
  U<-runif(length(p),0,1)
  outcomes<-U<p
  return(U)
}

I call the new version Nbs for “New Bernoulli Sampler”, or “Not Bull Shit”. And what a difference it made indeed!

library(rbenchmark)
p<-runif(1000)
res <- benchmark(bs(p), Nbs(p))
print(res)
test replications elapsed relative user.self sys.self user.child sys.child
2 Nbs(p)          100   0.007        1     0.008    0.000          0         0
1  bs(p)          100   1.099      157     1.080    0.016          0         0

157x faster! Now that’s a speedup to write home about.

Dan “The Man” Bernoulli