Gibbs sampling with Julia

Some time ago I wrote a post about Gibbs sampling using Matlab. There I showed that the JIT compiler of Matlab can get you very close to the speed of compiled C code if you know what you are doing, but that it is easy to screw up and get a very slow program as a result. More recently, I came across a new scientific programming language called Julia, which seems to be designed specifically with this kind of JIT compilation in mind. So I put Julia to the test, using the slow version of the Gibbs sampler from my last post:

 ```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ``` ```function gibbs2(n, thin)    x_samp = zeros(n,1)    y_samp = zeros(n,1)    x=0.0    y=0.0    for i=1:n       for j=1:thin          x=(y^2+4)*randg(3)          y=1/(1+x)+randn()/sqrt(2*x+2)       end       x_samp[i] = x       y_samp[i] = y    end    return x_samp, y_samp end```
```function gibbs2(n, thin)
x_samp = zeros(n,1)
y_samp = zeros(n,1)
x=0.0
y=0.0
for i=1:n
for j=1:thin
x=(y^2+4)*randg(3)
y=1/(1+x)+randn()/sqrt(2*x+2)
end
x_samp[i] = x
y_samp[i] = y
end
return x_samp, y_samp
end```
 ```1 2 ``` ```julia> @elapsed gibbs2(50000,1000) 7.6084020137786865```
```julia> @elapsed gibbs2(50000,1000)
7.6084020137786865```

The first thing to notice is that the Julia code looks very similar to the Matlab code from my last post, which is great for people familiar with that language. The second thing is that it is very fast and does not suffer from Matlab’s dumb JIT problems. In fact, this Julia code is even faster than the ‘fast version’ of the Matlab code from my last post. Way to go Julia!

6 thoughts on “Gibbs sampling with Julia”

1. Umberto on said:

Hi
thanks for the great post! On my machine it took 210 sec to run gibbs2 with Matlab and 14 sec with Julia. I used Matlab for Windows and run Julia on VM Virtualbox (Ubuntu). My machine is a Intel Core i7-2600 CPU 3.40 GHz 4GB RAM.

Not sure how you managed to make Julia run in 7-6 sec …?!

• Tim on said:

Thanks for sharing your timings! My PC is similar to yours, using Windows for the Matlab example and Ubuntu for Julia (no virtualization). Perhaps the VM added some overhead in your case? (although a factor of two does indeed seem high…) Also I built Julia from source. Did you perhaps use one of the binary distributions for Julia?

• Umberto on said:

Hi
thanks for the reply. My Julia has been built from source. Yeah the VM overhead is horrendously high (assuming this is the issue…). -.-’

2. Umberto on said:

New timings with the just released Julia for Windows (commit 49a5230831 released on 7th August).
And it’s a very good news! With the same machine as from my previous comment gibbs2(50000,1000) now runs in 7.65 seconds thus performing as it should (the previous — very first — Windows build was not impressive at all!).

Whoa! Go Julia!

• Tim on said:

Cool! Thanks for sharing!