Issue with affine transform and MvNormal

[ptiede]

Hi Chad,

I was just checking out the new version and noticed I was getting an inconsistent answer. Here is an MWE

using MeasureTheory
import Distributions as Dists
using LinearAlgebra

μ = zeros(2)
Σ = [1.0 0.0; 0.0 2.0]
Ω = [1.0 0.0; 0.0 0.5]

σC = cholesky(Σ)
ωC = cholesky(Ω)

dd = Dists.MvNormal(μ, Σ)

d1 = MvNormal{(:μ, :σ)}((μ=μ, σ=σC.L))
d2 = MvNormal{(:μ, :ω)}((μ=μ, ω=ωC.L))
d3 = Affine(AffineTransform((;μ, σ=σC.L)), Normal()^2)

# I expect this to give -0.5 log((2π)^2 * 2) ≈ -2.1845

logdensityof(dd, zeros(2)) # ≈ -2.1845
logdensityof(d1, zeros(2)) # ≈ -3.676
logdensityof(d2, zeros(2)) # ≈ -3.676
logdensityof(d3, zeros(2)) # ≈ -3.676

From my poking around, it looks like the log jacobian of the affine transform isn't being included in the density calculation, and inv(2pi) is being included twice: once in the basemeasure density and a second time in the proxy call.

[cscherrer]

Ouch, that's a big one - thanks for catching it. I should be able to fix this today (high priority, obviously). Here's an easy test to add

julia> v = diagm(rand(2))
2×2 Matrix{Float64}:
 0.341486  0.0
 0.0       0.569916

julia> z = zeros(2)
2-element Vector{Float64}:
 0.0
 0.0

julia> logdensityof(MvNormal(μ=z,σ=v), z) ≈ logdensityof(MvNormal(σ=v), z)
false

[cscherrer]

Thanks again @ptiede , this should be fixed in 0.15.1. Please reopen if you still see an issue :)