Add MvNormalMeanScalePrecision distribution

[albertpod]

This PR was initially aimed at addressing ReactiveBayes/ReactiveMP.jl#387, which it still does. The distribution in question is parametrized by the mean and scale parameter of the precision matrix.

Initially, I implemented it as part of the MultivariateNormalDistributionsFamily. However, the conversions between MvNormalMeanScalePrecision and other distributions in this "class" don't always hold.

During the process, @Nimrais suggested that this distribution could be particularly interesting for ExponentialFamilyProjections.jl. To make it more useful, we need to optimize methods related to the computation of the Fisher information matrix. I made a first attempt to improve performance by modifying the computation of kron(invη2, invη2). I believe further improvements are possible, but this serves as a starting point.

Any suggestions for additional optimizations to enhance the distribution's effectiveness are much welcome.

UPD: I added the piece of code that actually fixes the ReactiveBayes/ReactiveMP.jl#387

[albertpod]

ping @Nimrais

[Nimrais]

First, great work on implementing the MvNormalMeanScalePrecision distribution and integrating it into the ExponentialFamily.jl.

[Nimrais]

function BayesBase.rand(rng::AbstractRNG, dist::MvGaussianMeanScalePrecision{T}) where {T}
μ, γ = mean(dist), scale(dist)
return μ .+ (1 / γ) .* randn(rng, T, length(μ))
end

Avoid constructing the identity matrix I(length(μ)) and directly scale the random vector.
Use broadcasting with ., which is more efficient and avoids unnecessary allocations.

[Nimrais]

Similiarly to rand

function BayesBase.rand!(rng::AbstractRNG, dist::MvGaussianMeanScalePrecision, container::AbstractArray{T}) where {T <: Real}
    μ, γ = mean(dist), scale(dist)
    randn!(rng, container)
    @. container = μ + (1 / γ) * container
    return container
end

Btw I think rand just need to re-use rand!

[Nimrais]

@bvdmitri I think PR is ready for review, but I need some help with efficient implementation of the fisher. The only tests that are failing are once that checking that fisher in this parametrisation is really faster.

[albertpod]

Thanks for refactoring this, @Nimrais!

[bvdmitri]

@Nimrais ping, what needs to be done to finish this PR?

[Nimrais]

@bvdmitri The basic functionality is now implemented. The only remaining task is to implement the multiplication of the Fisher matrix with another matrix for the Arrowhead matrix structure in BayesBase. Currently, this multiplication is only done in our tests. There's already a generic method for all matrix structures using the getindex method, so implementing this method is the last thing we need to do.

[Nimrais]

@bvdmitri basically we need this PR ReactiveBayes/BayesBase.jl#25 be merged to finish this one