# Variable probability Bernoulli outcomes – Fast and Slow

**bayesianbiologist » Rstats**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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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.

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