The log-partition function for the continuous Bernoulli is not continuous.

[Nimrais]

I think there is a mistake,

logpartition(::VagueContinuousBernoulli, exponentialfamily::ExponentialFamilyDistribution{ContinuousBernoulli}) =
    log(2.0)

and it's supposed to be

logpartition(::VagueContinuousBernoulli, exponentialfamily::ExponentialFamilyDistribution{ContinuousBernoulli}) = 0

[albertpod]

Just wonder, @ismailsenoz, shouldn't we refrain from logpartitions resulting in constants?

[Nimrais]

@albertpod It's not possible for this distribution, because the expression is not well-defined at the value 0. But, if you will take it's limit you will obtain 0, not a log(2).

[Nimrais]

Maybe we can to add tiny under exponent but then the result is not precise: log((exp(0 + tiny) - 1)/(0 + tiny))

[bvdmitri]

What is vague/non-vague? Why do we need this? Why can't we just use the table from Wikipedia?

[bvdmitri]

Skimming through the code, I still don't understand the purpose of vague/non-vague stuff, the code is basically copy-pasted for both cases with minor differences. I would remove the vague/non-vague stuff entirely and just use the table from the Wikipedia, where logpartition is well defined

I see, the problem is the limit

[bvdmitri]

Wolfram tells me that the limit is not well-defined, I would probably simply remove all if-checks and let it fail if someone uses it with p=0.5 or make it a non proper exp family member

[Nimrais]

The limit is defined it's easy to check @bvdmitri

[Nimrais]

What is vague/non-vague? Why do we need this? Why can't we just use the table from Wikipedia?

Because this particular distribution is not yet added in the wikipage

[Nimrais]

@bvdmitri @ismailsenoz The guys defining its at $\lambda$ = 0.5 https://arxiv.org/pdf/1907.06845.pdf. And it is well behaving.

[bvdmitri]

The limit is defined it's easy to check

My bad

Because this particular distribution is not yet added in the wikipage

It is in the table

defining its at lambda = 0.5

Solving for specific case does not seem like a right solution (also in the current code). The function should be approximated with a different function in the whole region around that value, perhaps with linear, Fourier or bspline approximations then. Doing that right is not an easy task (the reason why StatsFuns.jl exists basically)

[Nimrais]

It is in the table

yes, you are right, I found it.

[bvdmitri]

The "right" way to fix numerically problematic functions usually look something like this 🥲, but I doubt we should spend a lot of time on it. Maybe there is already a package that computes it

[Nimrais]

Solving for specific case does not seem like a right solution (also in the current code). The function should be approximated with a different function in the whole region around that value, perhaps with linear, Fourier or bspline approximations then. Doing that right is not an easy task (the reason why StatsFuns.jl exists basically)

Agree, but it's still better then return 100% wrong value

[Nimrais]

I asked in Julia math slack channel, maybe someone already did it

[Nimrais]

😢

[Nimrais]

Jürgen Fuhrmann from this thread did $\frac{x}{e^{x}-1}$:

I have an implementation of the reciprocal (called Bernoulli function): https://github.com/j-fu/VoronoiFVM.jl/blob/faba3b6edbaf9d090feb3df60a06f2a4a14d5aaf/src/vfvm_functions.jl#L38 . See also the pluto notebook documenting the choices: https://github.com/j-fu/VoronoiFVM.jl/blob/master/pluto-examples/bernoulli.jl