`truncated` does not work with `Turing.jl`'s random variables

[Tobias-Thomas]

Hi,
I am currently building a Turing.jl model and want to use the draw of one random variable as the bound for another one, using the truncated function.
While the usage does not throw an error, it definitely does not seem to work (see MWE below).
I already saw this other issue, yet it was only about using random variables as parameters for the distribution. The case for using the draw of a random variable as a bound still seems to be not working.
Am I doing something wrong, or is there another way I could achieve using one random variable as the bound for another one?

a = 0:.05:1
b = 2 .- 1.5 * a + randn(21)
@model function truncate_mwe(x, y)
	intercept  ~ truncated(Normal(0, 1), 0, Inf)
	slope ~ truncated(Normal(0, 1), -intercept, Inf)

	for i in eachindex(y)
		y[i] ~ Normal(intercept + slope * x[i], 1)
	end
end
chain_mwe = sample(truncate_mwe(a,b), NUTS(), 1000)

For me, this chain always has some samples, for which intercept + slope < 0, which should not be the case as the maximum value for x in this case is 1.

Kind regards and thanks in advance for any help!

[devmotion]

Using Inf or -Inf as bounds for a truncated distribution leads to problems with ForwardDiff (the default automatic differentiation backend in Turing). Enabling NaN-safe mode (https://juliadiff.org/ForwardDiff.jl/dev/user/advanced/#Fixing-NaN/Inf-Issues) often fixes such issues. However, generally the better (and more efficient) approach is to construct the truncated distributions as truncated(Normal(0, 1); lower=0) and truncated(Normal(0, 1); lower=-intercept)).

Unfortunately, AFAICT applying this fix is not sufficient for your model since Turing does not support random variables whose support changes dynamically (in this case the support of slope changes depending on the value of intercept): TuringLang/Turing.jl#1558 TuringLang/Turing.jl#1708 As described in the linked issues you can fix this by defining a custom distribution with a custom bijector.

[yebai]

Unfortunately, AFAICT applying this fix is not sufficient for your model since Turing does not support random variables whose support changes dynamically

I think @torfjelde fixed this recently.

[Tobias-Thomas]

Unfortunately, AFAICT applying this fix is not sufficient for your model since Turing does not support random variables whose support changes dynamically

I think @torfjelde fixed this recently.

Do you mean that only leaving out the Inf values is sufficient? If yes, I do not see this happening. I just adjusted the slope in the MWE to be -5 and again get lots of values where intercept + slope < 0.

[Tobias-Thomas]

TuringLang/Turing.jl#1558 TuringLang/Turing.jl#1708 As described in the linked issues you can fix this by defining a custom distribution with a custom bijector.

Thank you for the explanation and the links! They look very promising and that definitely sounds like a solid workaround if it is not already natively supported.

[torfjelde]

I think @torfjelde fixed this recently.

Yeah, this should be working now, as long as the lower and upper kwargs are used:)

[Tobias-Thomas]

I think @torfjelde fixed this recently.

Yeah, this should be working now, as long as the lower and upper kwargs are used:)

Ok, after updating my packages it works like a charm, thank you so much for the help and the implementation!!