support intervals

[aplavin]

Add extension for IntervalSets (the most popular intervals package) to support its intervals where it makes sense in Distributions.
I defined and used this Uniform method a few times myself, others are included here for completeness.

No tests for now, looking for a general confirmation first.

[codecov-commenter]

Codecov Report

Attention: 5 lines in your changes are missing coverage. Please review.

Comparison is base (8e231ed) 85.98% compared to head (21b1d6c) 85.82%.
Report is 9 commits behind head on master.

Files	Patch %	Lines
ext/DistributionIntervalSetsExt.jl	0.00%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1809      +/-   ##
==========================================
- Coverage   85.98%   85.82%   -0.17%     
==========================================
  Files         144      145       +1     
  Lines        8648     8654       +6     
==========================================
- Hits         7436     7427       -9     
- Misses       1212     1227      +15     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[aplavin]

bump...

[devmotion]

I wonder if there is general interest for this functionality, the application seems a bit niche to me since most distributions have a fixed support that can't be adjusted based on a given interval. My gut feeling is that it is easy enough to extract the endpoints of an interval and call the standard constructors if one wants to construct e.g. a Uniform distribution on a given interval.

[aplavin]

Many interval operations are "easy enough" to do without a special interval type at all, by working with endpoints directly. The whole point of an interval type (same with many other types, such as Pair or NamedTuple, or even Uniform itself) is that it adds semantics to a bunch of values, and allows to keep this semantic across function calls.

We use these functions not because they are hard to implement without a special type (they're not!), but because they are natural and convenient:

julia> i = 1..3

julia> 2 ∈ i
true

julia> range(i, length=5)
1.0:0.5:3.0

Isn't it natural to create a uniform distribution on a given interval?..

Uniform(i)
# instead of
Uniform(leftendpoint(i), rightendpoint(i))

[aplavin]

most distributions have a fixed support that can't be adjusted based on a given interval

Not sure if I understand this part. Of course it doesn't make sense to have a Normal(interval) constructor, but for some distributions such a constructor is a good fit.

[chelate]

I just want to point out that intervals are somewhat fundamental objects in probability (the Borel algebra), and that prob(interval,dist) = cdf(dist,interval.upper) - cdf(dist,interval.lower) or similar could be pretty neat. Likewise conditional probabilities, empirical samplers, histograms, all kinds of stuff!

[aplavin]

Yes, this kind of probability calculations is convenient sometimes, but orthogonal to this PR. Here, I add intervals support to already existing functions, no new functions added.

For playing with distributions and probabilities, I have a snippet defining an interface similar but more general than your prob(...) suggestion.
Usage:

ℙ(∈(0..1), Normal(0, 1))
ℙ(<(1), Normal(0, 1))
...

Some function definitions

ℙ(f::Base.Fix2{typeof(<=)}, d::UnivariateDistribution) = cdf(d, f.x)
ℙ(f::Base.Fix2{typeof(> )}, d::UnivariateDistribution) = ccdf(d, f.x)

function ℙ(f::Base.Fix2{typeof(∈), <:Interval}, d::UnivariateDistribution)
    Pr = isrightclosed(f.x) ? ℙ(<=(rightendpoint(f.x)), d) : ℙ(<(rightendpoint(f.x)), d)
    Pl = isleftclosed(f.x)  ? ℙ(<(leftendpoint(f.x)), d)   : ℙ(<=(leftendpoint(f.x)), d)
    return Pr - Pl
end

Can potentially make sense to add to DIstributions as well, but not in this PR as these are completely unrelated. Or just make a separate package with the `ℙ` function, it doesn't need to live here in `Distributions`.

[aplavin]

Gentle bump...
This PR adds support for intervals arguments to existing methods where it makes sense and is totally unambiguous. Everything else including @chelate's suggestions is out of scope here and can easily live in a separate package.

[devmotion]

I guess such definitions might be convenient for someone working with IntervalSets, but my feeling is that these should rather be put in an extension of IntervalSets (similar to existing extensions for Random, Statistics, and StatsBase).

[aplavin]

Oh, sorry, I forgot to explicitly state the motivation to put this into Distributions indeed!
This extension is much more likely to require changes due to changes in Distributions, than due to changes in IntervalSets. For example, when new distributions/functions are added here.
Also, IntervalSets is a much much more lightweight package.

[devmotion]

My concern is that putting these definitions in an extension in Distributions adds maintenance burden for developers that seemingly so far have never expressed a desire to use IntervalSets for constructing the few univariate distributions whose support is an interval that fully characterizes the parameters of this distribution type. The use case still seems quite limited to me, and hence I think one has not be too worried about new distributions. Since the PR also only uses exported and official APIs, I don't think potential breakages are a problem either.

To me it seems contributors of IntervalSets are much more interested in such a functionality than developers of Distributions, so I guess an extension in IntervalSets would be preferable.

[aplavin]

In case others come looking for this functionality: the interval support (this PR) is available in https://github.com/JuliaAPlavin/DistributionsExtra.jl. Not sure if I want to register that package yet...

It has more than that, btw – including what @chelate suggested above, stuff like ℙ(>(0), Poisson(1)) or ℙ((@o abs(_) > 2), Normal(0, 1)).