Sample dependent variables in Turing

Specific Domains Probabilistic programming
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1

I’d like to sample two variables X1 ~ Uniform(0,1) and X2 ~ Uniform(0, X1)

using Turing
@model function model()
X1 ~ Uniform(1e-5, 1)
X2 ~ Uniform(0, X1)
end
my_model = model(); sample(my_model, NUTS(), 10000)

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However, while the distribution of X1 looks correct (that is it follows Uniform(0,1)), the distribution of X2 is very strange and each time it changes a lot. Analytically the mean of X2 should be 0.25 but this result is never reached. Can anyone help me figure out where I did wrong?

2

Could this be a matter of not having enough samples? I increased the chain length 100-fold to 1_000_000 and am seeing stats like

Summary Statistics
  parameters      mean       std      mcse      ess_bulk      ess_tail      rhat   ess_per_sec
      Symbol   Float64   Float64   Float64       Float64       Float64   Float64       Float64

          X1    0.4999    0.2887    0.0003   796644.8328   663422.4909    1.0000    19973.0440
          X2    0.2497    0.2201    0.0002   765366.0740   647466.4402    1.0000    19188.8400
3

Thanks so much! That’s interesting. But I still have this problem.

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Actually such a problem doesn’t exist if X2 ~ Normal(X1, 1) or Exponential(X1). Seems only happen if X2 ~ Uniform(0, X1).

what version of turing are you using? Mine are v0.29.3 and v0.30, with both having the same issue. Did you see the same problem when sample size is 10^4 (actually I think that’s big enough if I am not mistaken).

Thanks so much!

4

I thought I was getting wildly varying means at 10k samples but I’m not, my bad. Indeed, 10k seems plenty.

I’m using Turing v0.32.2 and Distributions v0.25.109.

5

Ah yes, this was a bug that was recently fixed. In short, the inference was actually performed correctly, but there was a bug in the code transforming the variables to the format we present it to the end-user. If you go to Turing 0.32 everything should work just fine again:)

Can confirm this works on my end with Turing.jl@0.32.3 and 10k samples (reproducible).

Did you see the same problem when sample size is 10^4 (actually I think that’s big enough if I am not mistaken).

Recommend looking at effective sample size (ESS) in the chain when considering “how many samples do I have”. Even if you run 10k iterations, the sampler could get stuck, but that would be indicated in the ESS.

When I run your code (again, on v0.32.3), with 10k iterations I consistently get >5k ESS, which is pleeeeenty for evaluating whether we’re getting the mean correctly:) And in my case, I consistently get 0.5 and 0.25 as expected :+1:

2 Likes
6

thank you so much! the newest version got it correct. Also thanks for ESS!

7

Glad to hear:)

Would you mind marking the answer as the “solution”? That way others who arrive at the same issue can easily see the answer:)

8

Thank you for the reminder. Marked!

1 Like