linear transformations on MvNormal

[goretkin]

Are these functions within the scope of the package? These seem harmless

+(x::AbstractVector,n::MvNormal) = MvNormal(n.μ+x,n.Σ)
+(n::MvNormal,x::AbstractVector) = MvNormal(n.μ+x,n.Σ)
Xt_A_X
*(A::AbstractMatrix,n::MvNormal) = MvNormal(A*n.μ,  PDMats.Xt_A_X(n.Σ,A)  )

More contentious is allowing +(x::MvNormal,y::MvNormal), assuming independence.

My main motivation was from seeing the StateSpace package that @ElOceanografo wrote. For example: https://github.com/ElOceanografo/StateSpace.jl/blob/master/src/KalmanFilter.jl#L49 . Having functions for linear transformations of Multivariate Normal distributions might improve readability in only a minor way, but they might be worth including in Distributions anyway.

[johnmyleswhite]

Dup of #298?

[lindahua]

Linear transformations are more than scaling. I think this issue can stay as a separate one.

[mschauer]

I am running into the same problem trying to port a Kalman filter now from
https://github.com/mschauer/GaussianDistributions.jl/blob/master/src/GaussianDistributions.jl
to Distributions. How do you see this?

[simonbyrne]

It would be good to have some way to do this, at least for constants. Mathematically, I'm a bit reluctant to overload +/* directly: the objects are intended to be distributions, not random variables. But maybe that isn't such a big deal?

Alternatively we could overload map (e.g. so that you would do map(x -> x + k, d)), but that would require much more "plumbing" to get it to work.

[goretkin]

I hadn't considered making the distinction between an object that represents a distribution and an object that represents a random variable following that distribution, but I agree that the distinction certainly can exist. Can we think of a case where this distinction serves a purpose?

…

On Fri, Oct 12, 2018 at 7:00 PM Simon Byrne ***@***.***> wrote: It would be good to have some way to do this, at least for constants. Mathematically, I'm a bit reluctant to overload +/* directly: the objects are intended to be distributions, not random variables. But maybe that isn't such a big deal? Alternatively we could overload map (e.g. so that you would do map(x -> x + k, d)), but that would require much more "plumbing" to get it to work. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <#307 (comment)>, or mute the thread <https://github.com/notifications/unsubscribe-auth/AAjds8jFMo0OkbxJZrVrbLYLONz-Z6dRks5ukR71gaJpZM4C5dOC> .

[mschauer]

For example you would not overload +(A::RandomVariable,B::RandomVariable) because the result depends on whether RVs are dependent and the independent sum deserves a new symbol like ⊕. But +(A::Vector, B::MvNormal) and *(A::Matrix B::MvNormal) can only mean one thing imho.

[simonbyrne]

I mean, the only other interpretation it could mean would be transforming it as a measure, but (a) that isn't very useful (since it would no longer be a probability measure), and (b) we don't treat it as a measure in other contexts, e.g. defining (d::Distribution)(x::Interval) to get the probability of an interval.

independent sum deserves a new symbol like ⊕

That's a great idea!

[mschauer]

One thing, for scalar λ the expression λ*D1 + (1-λ)*D2 could denote a mixture distribution.

[matbesancon]

@JuliaRegistrator register()

[JuliaRegistrator]

Registration pull request created: JuliaRegistries/General/7761

After the above pull request is merged, it is recommended that a tag is created on this repository for the registered package version.

This will be done automatically if Julia TagBot is installed, or can be done manually through the github interface, or via:

git tag -a v0.22.1 -m "<description of version>" 16ba0b4cb040f87a098377bd01fd62161c6c4491
git push origin v0.22.1