Constant Distribution

[jpfairbanks]

I'm working on something that involves both stochastic and deterministic functions and it would be nice to have a Constant <: Distribution that satisfies the Distributions API but always returns its parameter. Would that be something welcome in Distributions.jl?

[johnczito]

This has come up before (#1040), and there's a PR outstanding (#861). Depending on your needs, you can get this behavior by creating a Normal with zero variance, or a DiscreteNonParametric with one support point. To get a vector-valued constant you can define a Product distribution based on a vector of those.

[devmotion]

Fixed by #1231.

[oschulz]

I have a ConstValueDist in ValueShapes.jl that is very similar to the new Dirac, but it can also handle non-univariate values. Wouldn't mind to get rid of it in favor of Dirac though - would it be acceptable to add a type parameter for the variate form to Dirac? If so, I could put a PR together.

[devmotion]

Sure, it's indeed a bit limiting that it only works with real numbers currently.

[oschulz]

Ok, I'll see if I can port that over from https://github.com/oschulz/ValueShapes.jl/blob/master/src/const_value_dist.jl .

I'll have to see how I handle NamedTupleVariates though, since that's a ValueShape-specific thing so far (it supports dists with actual named NamedTuples as variates and can reshape them to flat Multivariate dists an vice-versa). Having Distributions.Dirac(x::NamedTuple{names}) = ... in ValueShapes would be type-piracy, obviously.

In principle, could there be room in Distributions.jl for declaring a variate type for NamedTuples (and maybe for structs as well), next to ArrayLikeVariate (#1313)?

[devmotion]

I think a possible approach would be to define functions variateform(::Real) = ArrayLikeVariate{0} and variateform(::Array{<:Real,N}) where {N} = ArrayLikeVariate{N} in Distributions, and then just use variateform in the constructor of Dirac. Then packages such as ValueShapes.jl could define their own variate types and could use Dirac if they just implement variateform for the types that their variate form covers.

[oschulz]

Oh, yes, having a generic function variateform in Distributions would be very nice. But I guess for Base types like NamedTuple we'd still need to define the respective method and variate type in Distributions, right? If ValueShapes would define variateform(::NamedTuple{names}) it would still be type piracy. I would like to move part of ValueShapes support for non-array-like variates to Distributions though, if they would be judged acceptable.